Linear Equation In One Variable
Class 8th Mathematics RD Sharma Solution
- 9 1/4 = y-1 1/3 Solve each of the following equations and also verify your…
- 5x/3 + 2/5 = 1 Solve each of the following equations and also verify your…
- x/2 + x/3 + x/4 = 13 Solve each of the following equations and also verify your…
- x/2 + x/8 = 1/8 Solve each of the following equations and also verify your…
- 2x/3 - 3x/8 = 7/12 Solve each of the following equations and also verify your…
- (x+2) (x+3) + (x-3) (x-2) - 2x (x+1) = 0 Solve each of the following equations…
- x/2 - 4/5 + x/5 + 3x/10 = 1/5 Solve each of the following equations and also…
- 7/x + 35 = 1/10 Solve each of the following equations and also verify your…
- 2x-1/3 - 6x-2/5 = 1/3 Solve each of the following equations and also verify your…
- 13 (y-4) - 3 (y-9) - 5 (y+4) = 0 Solve each of the following equations and also…
- 2/3 (x-5) - 1/4 (x-2) = 9/2 Solve each of the following equations and also…
- 2x+5/3 = 3x-10 Solve each of the following equations and also check your result…
- a-8/3 = a-3/2 Solve each of the following equations and also check your result…
- 7y+2/5 = 6y-5/11 Solve each of the following equations and also check your…
- x-2x+2 - 16/3 x+5 = 3 - 7/2 x Solve each of the following equations and also…
- 1/2 x+7x-6 = 7x + 1/4 Solve each of the following equations and also check your…
- 3/4 x+4x = 7/8 + 6x-6 Solve each of the following equations and also check your…
- 7/2 x - 5/2 x = 20/3 x+10 Solve each of the following equations and also check…
- 6x+1/2 + 1 = 7x-3/3 Solve each of the following equations and also check your…
- 3a-2/3 + 2a+3/2 = a + 7/6 Solve each of the following equations and also check…
- x - (x-1)/2 = 1 - (x-2)/3 Solve each of the following equations and also check…
- 3x/4 - (x-1)/2 = (x-2)/3 Solve each of the following equations and also check…
- 5x/3 - x-1/4 = x-3/5 Solve each of the following equations and also check your…
- (3x+1)/16 + (2x-3)/7 = (x+3)/8 + (3x-1)/14 Solve each of the following…
- (1-2x)/7 - (x-1)/4 = (x-3)/8 = 3/2 + x/4 Solve each of the following equations…
- 9x+7/2 - (x - x-2/7) = 36 Solve each of the following equations and also check…
- 0.18 (5x-4) = 0.5x+0.8 Solve each of the following equations and also check…
- 2/3x - 3/2x = 1/12 Solve each of the following equations and also check your…
- 4x/9 + 1/3 + 13/108 x = 8x+19/18 Solve each of the following equations and also…
- (45-2x)/15 - (4x+10)/5 = (15-14x)/9 Solve each of the following equations and…
- 5 (7x+5/3) - 23/3 = 13 - 4x-2/3 Solve each of the following equations and also…
- 7x-1/4 - 1/3 (2x - 1-x/2) = 10/3 Solve each of the following equations and also…
- 0.5 (x-0.4)/0.35 - 0.6 (x-2.71)/0.42 = x+6.1 Solve each of the following…
- 6.5x + 19.5x-32.5/2 = 6.5x+13 + (13x-26/2) Solve each of the following…
- 6.5x + 19.5x-32.5/2 = 6.5x+13 + (13x-26/2) Solve each of the following…
- [(2x+3) + (x+5)]^-2 + [(2x+3) - (x+5)]^-2 = 10x^2 + 92 Solve each of the…
- 2x-3/3x+2 = - 2/3 Slove the following equations and verify your answer:…
- 2-y/y+7 = 3/5 Slove the following equations and verify your answer:…
- 5x-7/3x = 2 Slove the following equations and verify your answer:…
- 3x+5/2x+7 = 4 Slove the following equations and verify your answer:…
- 2y+5/y+4 = 1 Slove the following equations and verify your answer:…
- 2x+1/3x-2 = 5/9 Slove the following equations and verify your answer:…
- Solve the following equations and verify your answer: 1-9y/19-3y = 5/8…
- 2x/3x+1 = 1 Slove the following equations and verify your answer:…
- y - (7-8y)/9y - (3+4y) = 2/3 Slove the following equations and verify your…
- 6/2x - (3-4x) = 2/3 Slove the following equations and verify your answer:…
- 2/3x - 3/2x = 1/12 Slove the following equations and verify your answer:…
- 3x+5/4x+2 = 3x+4/4x+7 Slove the following equations and verify your answer:…
- 7x-2/5x-1 = 7x+3/5x+4 Slove the following equations and verify your answer:…
- Solve the following equations and verify your answer: (x+1/x+2)^2 = x+2/x+4…
- (x+1/x-4)^2 = x+8/x-2 Slove the following equations and verify your answer:…
- 9x-7/3x+5 = 3x-4/x+6 Slove the following equations and verify your answer:…
- x+2/x+5 = x/x+6 Slove the following equations and verify your answer:…
- 2x - (7-5x)/9x - (3+4x) = 7/6 Slove the following equations and verify your…
- 15 (2-x) - 5 (x+6)/1-3x = 10 Slove the following equations and verify your…
- x+3/x-3 + x+2/x-2 = 2 Slove the following equations and verify your answer:…
- Solve the following equations and verify your answer: (x+2) (2x-3) - 2x^2 +…
- x^2 - (x+1) (x+2)/5x+1 = 6 Slove the following equations and verify your…
- (2x+3) - (5x-7)/6x+11 = - 8/3 Slove the following equations and verify your…
- Find a positive value of x for which the given equation is satisfied: (i) x^2 -…
- Four-fifth of a number is more than three-fourth of the number by 4. Find the…
- The difference between the squares of two consecutive numbers is 31. Find the…
- Find a number whose double is 45 greater than its half.
- Find a number such that when 5 is subtracted from 5 times that number, the…
- A number whose fifth part increased by 5 is equal to its fourth part diminished…
- A number consists of two digits whose sum is 9. If 27 is su btracted from the…
- Divide 184 into two parts such that one-third of one part may exceed one-seventh…
- The numerator of a fraction is 6 less than the denominator. If 3 is added to the…
- A sum of Rs 800 is in the form of denominations of Rs 10 and Rs 20. If the total…
- Seeta Devi has Rs 9 in fifty- paise and twenty five-paise coins. She has twice…
- Sunita is twice as old as Ashima. If six years is subtracted from Ashimas age…
- The ages of Sonu and Monu are in the ratio 7:5 Ten years hence, the ratio of…
- Five years ago a man was seven times as old as his son. Finve years hence, the…
- I am currently 5 times as old as his son. In 6 years time I will be three times…
- I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes…
- At a party, colas, squash and frut juice were offered to guests. A fourth of…
- There are 180 multiple choice questions in a test. If a candidate gets 4 marks…
- A labourer is engaged for 20 days on the condition that he will receive Rs 60…
- Ravish has three boxes whose total weight is 60 1/2 Kg. Box B weighs 3 1/2 kg…
- The numerator of a rational number is 3 less than the denominator. If the…
- In a rational number, twice the numerator is 2 more than the denominator If 3…
- The distance between two stations is 340 km. Two trains start simultaneously…
- A steamer goes downstream from one point another in 9 hours. It covers the same…
- Bhagwanti inherited Rs 12000.00. She invested part of it as 10% and the rest at…
- The length of a rectangle exceeds its breadth by 9 cm. If length and breadth…
- The sum of the ages of Anup and his father is 100. When Anup is as old as his…
- A lady went shopping and spent half of what she had on buying hankies and gave…
Exercise 9.1
Question 1.Solve each of the following equations and also verify your solution:
Answer:
On transposing 
to right hand side (RHS)
Question 2.
Solve each of the following equations and also verify your solution:
Answer:
On transposing 
to right hand side (RHS)
On cross-multiplication, we get,
Check:
Take LHS:
⇒
= 
= 1
We got LHS=RHS
Question 3.
Solve each of the following equations and also verify your solution:
Answer:
LCM of 2, 3, and 4 = 12
On cross-multiplication, we get,
Check:
Take LHS:
We got LHS=RHS
Question 4.
Solve each of the following equations and also verify your solution:
Answer:
LCM of 2 and 8 is 8
On cross-multiplication, we get,
Check:
Take LHS:
We got LHS=RHS
Question 5.
Solve each of the following equations and also verify your solution:
Answer:
LCM of 3 and 8 is 24
On cross-multiplication, we get,
Check:
Take LHS:
We got LHS=RHS
Question 6.
Solve each of the following equations and also verify your solution:
Answer:
On opening the brackets we get,
x2 + 5x + 6 + x2 - 5x +6 - 2x2 - 2x =0
On dividing by -2 we get,
x - 6 = 0
x = 6
Check:
Take LHS:
On substituting x = 6
We got LHS=RHS
Question 7.
Solve each of the following equations and also verify your solution:
Answer:
On Transposing 
to RHS
LCM of 2 and 5 is 10
Check:
Take LHS:
= 
We got LHS=RHS
Question 8.
Solve each of the following equations and also verify your solution:
Answer:
On Transposing 35 to RHS
Check:
Take LHS:
We got LHS=RHS
Question 9.
Solve each of the following equations and also verify your solution:
Answer:
On cross multiplication, we get
Check:
We got LHS=RHS
Question 10.
Solve each of the following equations and also verify your solution:
Answer:
13(y - 4) - 3(y - 9) - 5(y + 4) = 0
13y - 52 - 3y + 27 - 5y - 20 = 0
5y = 45
y = 9
Check:
13(y - 4) - 3(y - 9) - 5(y + 4) = 013(9 - 4) - 3(9 - 9) - 5(9 + 4)
13(5) - 0 - 5(13)
= 0
We got LHS = RHS
Hence, verified.
Question 11.
Solve each of the following equations and also verify your solution:
Answer:
On transposing constant terms to RHS
On cross multiplication
Check:
Taking LHS
We got LHS=RHS
Exercise 9.2
Question 1.Solve each of the following equations and also check your result in each case:
Answer:
On transposing 3x to RHS
On cross multiplication
Check:
Taking LHS
Taking RHS
We got LHS=RHS
Question 2.
Solve each of the following equations and also check your result in each case:
Answer:
On cross multiplication
2(a - 8) = 3(a - 3)2a - 16 = 3a - 3
On transposing constant terms to RHS and variables to LHS, we get
2a - 3a = 16 - 9-a = 7
a = -7
Check:
Taking LHS
On substituting a = -7, we get
Taking RHS
On substituting a = -7, we get
We got LHS = RHS
Question 3.
Solve each of the following equations and also check your result in each case:
Answer:
On cross multiplication
On transposing constant terms to RHS and variables to LHS, we get
Check:
Taking LHS
On substituting a = -1, we get
Taking RHS
On substituting a = -1, we get
We got LHS=RHS
Question 4.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing constant terms to RHS and variables to LHS, we get
On taking LCM of 2 and 3, we get 6
Check:
Taking LHS
On substituting
, we get
Taking RHS
On substituting, we get
We got LHS=RHS
Question 5.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing constant terms to RHS and variables to LHS, we get
Check:
Taking LHS
On substituting
, we get
Taking RHS
On substituting, we get
We got LHS=RHS
Question 6.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing constant terms to RHS and variables to LHS, we get
Check:
Taking LHS
On substituting
, we get
Taking RHS
On substituting, we get
We got LHS=RHS
Question 7.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS, we get
LCM of 2 and 3 is 6,
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 8.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS and 1 to RHS, we get
LCM of 2 and 3 is 6,
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 9.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS, we get
LCM of 2 and 3 is 6,
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 10.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS, we get
LCM of 2 and 3 is 6,
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 11.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS, we get
LCM of 2, 3 and 4 is 12,
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 12.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS, we get
LCM of 3, 4 and 5 is 60,
Check:
Taking LHS
On taking LCM of 3 and 4; substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 13.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS, we get
LCM of 7, 8, 14 and 16 is 112
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 14.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS, we get
LCM of 7 and 8 is 56
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 15.
Solve each of the following equations and also check your result in each case:
Answer:
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 16.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS and 0.80 to RHS, we get
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 17.
Solve each of the following equations and also check your result in each case:
Answer:
On cross multiplication, we get
Check:
Taking LHS
On substitutingwe get
We got LHS=RHS
Question 18.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS and 
to RHS, we get
On cross multiplication, we get
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 19.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS, we get
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 20.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
to LHS and 
, to RHS we get
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
, we get
We got LHS=RHS
Question 21.
Solve each of the following equations and also check your result in each case:
Answer:
Taking LCM of 4 and 6
On cross ultiplication, we get
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 22.
Solve each of the following equations and also check your result in each case:
Answer:
LCM of 0.35 and 0.42 is 2.10
Check:
Taking LHS
On substituting
we get
Taking RHS
On substitutingwe get
We got LHS=RHS
Question 23.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
and 
to LHS
On cross multiplication, we get
Check:
Taking LHS
On substituting
we get
Taking RHS
On substitutingwe get
We got LHS=RHS
Question 24.
Solve each of the following equations and also check your result in each case:
Answer:
On transposing 
and 
to LHS
On cross multiplication, we get
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
we get
We got LHS=RHS
Question 25.
Solve each of the following equations and also check your result in each case:
Answer:
On opening brackets
On transposing 
to LHS and 68 to RHS
Check:
Taking LHS
On substituting
we get
Taking RHS
On substituting
we get
We got LHS=RHS
Exercise 9.3
Question 1.Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
On transposing 
to LHS and 
to RHS
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 2.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
On transposing 
to LHS and 
to RHS
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 3.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
On transposing 
to LHS and -7 to RHS
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 4.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
On transposing 
to LHS and 5 to RHS
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 5.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
On transposing 
to LHS and 5 to RHS
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 6.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
On transposing 
to LHS and 9 to RHS
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 7.
Solve the following equations and verify your answer:
Answer:
On cross multiplication, we get
8(1 - 9y) = 5(19 - 3y)
-72y + 8 = 95 - 15y
On transposing - 15y to LHS and 8 to RHS
-72y + 15y = 95 - 8-57y = 87
Check:
Taking LHS
On substituting
we get
We got LHS = RHS
Question 8.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
On transposing 
to LHS and 1 to RHS
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 9.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
On transposing 
to LHS and -21 to RHS
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 10.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 11.
Slove the following equations and verify your answer:
Answer:
LCM of 2 and 3 is 6
On cross multiplication, we get
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 12.
Slove the following equations and verify your answer:
Answer:
On transposing 
to LHS
On taking LCM of the denominators, we get
On cross multiplication, we get
On opening the brackets:
Check:
Taking LHS
On substituting
we get
Taking RHS
On substitutingwe get
We got LHS=RHS
Question 13.
Slove the following equations and verify your answer:
Answer:
On transposing 
to LHS
On taking LCM of the denominators, we get
On cross multiplication, we get
On opening the brackets:
Check:
Taking LHS
On substituting
we get
Taking RHS
On substitutingwe get
We got LHS=RHS
Question 14.
Solve the following equations and verify your answer:
Answer:
On transposing 
to LHS
On taking LCM of the denominators, we get
On cross multiplication, we get
On opening the brackets:
On opening the brackets:
Check:
Taking LHS
On substituting
we get
Taking RHS
On substitutingwe get
We got LHS=RHS
Question 15.
Slove the following equations and verify your answer:
Answer:
On transposing 
to LHS
On taking LCM of the denominators, we get
On cross multiplication, we get
On opening the brackets:
Check:
Taking LHS
On substituting
we get
Taking RHS
On substitutingwe get
We got LHS=RHS
Question 16.
Slove the following equations and verify your answer:
Answer:
On transposing 
to LHS
On taking LCM of the denominators, we get
On cross multiplication, we get
On opening the brackets:
Check:
Taking LHS
On substitutingwe get
Taking RHS
On substitutingwe get
We got LHS=RHS
Question 17.
Slove the following equations and verify your answer:
Answer:
On transposing 
to LHS
On taking LCM of the denominators, we get
On cross multiplication, we get
On opening the brackets:
Check:
Taking LHS
On substituting
we get
Taking RHS
On substitutingwe get
We got LHS=RHS
Question 18.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 19.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
Check:
Taking LHS
On substitutingwe get
We got LHS=RHS
Question 20.
Slove the following equations and verify your answer:
Answer:
On taking LCM of denominators
On cross multiplication, we get
On opening brackets, we get
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 21.
Solve the following equations and verify your answer:
Answer:
On cross multiplication, we get
2x - 10 = x2x - x = 10
x = 10
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 22.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 23.
Slove the following equations and verify your answer:
Answer:
On cross multiplication, we get
Check:
Taking LHS
On substituting
we get
We got LHS=RHS
Question 24.
Find a positive value of x for which the given equation is satisfied:
(i) 
(ii) 
Answer:
(i) 
On cross multiplication, we get
On transposing 
to LHS and -81 to RHS
(ii) 
On cross multiplication, we get
On transposing 
to LHS and 8 to RHS
Exercise 9.4
Question 1.Four-fifth of a number is more than three-fourth of the number by 4. Find the number.
Answer:
Let the number is 
According to the question:
Three-fourth of the number is = 
Fourth-fifth of the number is = 
LCM of 5 and 4 is 20
Therefore number is 80
Question 2.
The difference between the squares of two consecutive numbers is 31. Find the numbers.
Answer:
Let the two consecutive numbers are x - 1 and x
According to the question:
[As, (a - b)2 = a2 + b2 + 2ab]
x = 16
Therefore two consecutive numbers are: (16 - 1) and 16 = 15 and 16
Question 3.
Find a number whose double is 45 greater than its half.
Answer:
Let the number is
According to the question:
Therefore the number is 30
Question 4.
Find a number such that when 5 is subtracted from 5 times that number, the result is 4 more than twice the number.
Answer:
Let the number is "x"
Then, five times the number will be = 5x
And, two times the number will be = 2x
then, According to the question:
5x - 5 = 2x + 4
On transposing 2x to LHS and -5 to RHS,
5x - 2x = 5 + 4
3x = 9
x = 9/3
x = 3
Therefore the number is 3
Question 5.
A number whose fifth part increased by 5 is equal to its fourth part diminished by 5. Find the number.
Answer:
Let the number is
According to the question:
On transposing 
to RHS and -5 to LHS
Therefore the number is 200
Question 6.
A number consists of two digits whose sum is 9. If 27 is su btracted from the number the digits are reversed. Find the number.
Answer:
Let the one didgit of a two digit number is
Other digit is 9-x
Original two digit number is 
Number obtained after interchanging the digits is 
)
According to the question:
)
Therefore the number is 
Question 7.
Divide 184 into two parts such that one-third of one part may exceed one-seventh of another part by 8.
Answer:
Let the one number is x
Other number is 184 - x
According to the question:
one-third of one part may exceed one-seventh of another part by 8.
Therefore one number is 72
Other number is 184-72 = 112
Question 8.
The numerator of a fraction is 6 less than the denominator. If 3 is added to the numberator, the fraction is equal to 
. What is the original fraction equal to?
Answer:
Let the denominator is 
Numerator is 
Fraction is : 
According to the question:
On cross multiplication, we get
Therefore denominator is = 9
Numerator is = 
Fraction is = 
Question 9.
A sum of Rs 800 is in the form of denominations of Rs 10 and Rs 20. If the total number of notes be 50. Find the number of notes of each type.
Answer:
Let the number of notes of Rs 10 are
Number of notes of Rs 20 are 
Amount due to Rs 10 notes = 
Amount due to Rs 20 notes = 
According to the question total amount = Rs 800
Therefore the number of notes of Rs 10 are 
Number of notes of Rs 20 are 
Question 10.
Seeta Devi has Rs 9 in fifty- paise and twenty five-paise coins. She has twice as may twenty- five paise coins as she has fifty- paise coins. How many coins of each kind does she have?
Answer:
Let the number of coins of fifty paise are
Number of coins of twenty five paise are
Amount due to fifty paise coins = 
Amount due to twenty five paise coins = 
According to the question total amount = Rs 9
Therefore the number of coins of fifty paise are 
Number of coins of twenty five paise are 
Question 11.
Sunita is twice as old as Ashima. If six years is subtracted from Ashima’s age and four years added to Sunita’s age, then Sunita will be four times Ashim’s age. How old were they two years ago?
Answer:
Let the present age of Ashima is x years
Present age of Sunita is 2x years
Ashima’s new age = (x - 6) years
Sunita’s new age = (2x + 4) years
According to the question:
Therefore the age of Ashima is 14 years
Age of Sunita is 28 years
Two years agp,
age of ashima = 14 - 2 = 12 years
age of Sunita = 28 - 2 = 26 years
Question 12.
The ages of Sonu and Monu are in the ratio 7:5 Ten years hence, the ratio of their ages will be 9:7 find their present ages.
Answer:
Let the present age of Sonu is 
years
Present age of Monu is 
years
Sonu’s age after 10 years = 
years
Monu’s age after 10 years = 
years
According to the question:
On cross multiplication, we get
Therefore present age of Sonu is 
years
Present age of Monu is 
years
Question 13.
Five years ago a man was seven times as old as his son. Finve years hence, the father will be three times as old as his son. Find their present ges.
Answer:
Five years ago let the age of son was 
years
Five years ago the age of man was years
After five years the age of son is 
years
After five years the the age of man is 
years
According to the question:
Five years hence, the relation in their ages is:
Therefore present age of man is 
years
Present age of son is 
years
Question 14.
I am currently 5 times as old as his son. In 6 years time I will be three times as old as he will be then. What are our ages now?
Answer:
Let the present age of Son is years
Present age of father is years
Son’s age after 6 years = 
years
Father’s’s age after 6 years = 
years
According to the question:
Therefore present age of Son is 
years
Present age of father is 
years
Question 15.
I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes that I have is ten more than the number of five rupee notes, how many notes do I have in each denomination?
Answer:
Let the number of five rupess notes are
Number of ten rupees notes are 
Amount due to five rupees notes = 
Amount due to ten rupees notes = 
According to the question total amount = Rs 1000
Therefore the number of five rupess notes are 
Number of ten rupees notes are 
Question 16.
At a party, colas, squash and frut juice were offered to guests. A fourth of the guests drank colas, a thirk squash, two fifths drank fruit juice and just three did not drink any thing. How many guests were in all?
Answer:
Let the number of guests are
Number of guests who drank colas are
Number of guests who drank squash are 
Number of guests who drank fruit juice are 
Number of guests who didn’t drink anyting are 3
LCM of 3, 4 and 5 is 60
Therefore the number of guests were 180
Number of ten rupees notes are
Question 17.
There are 180 multiple choice questions in a test. If a candidate gets 4 marks for every correct answer and for every unattempted or wrongly answered question one mark is deducted from the total score of correct answers. If a candidate scored 450 marks in the test, how many questions did he answer correctly?
Answer:
Let the number of correct answers are x
Number of wrong answered questions are (180 - x)
Total score due to right answers = 4x
Marks deducted due to wrong answers = 1(180 - x) = 180 - x
According to question:
Therefore number of correct questions are 126
Question 18.
A labourer is engaged for 20 days on the condition that he will receive Rs 60 for each day, he works and he will be fined Rs 5 for each day, he is absent. If he receives Rs 745 in all for how many days he remained absent?
Answer:
Let the number of absent days are
Number of present days = 
Wage for one day work = Rs 60
Fine for absent day = Rs 5
According to the question:
Therefore number of absent days are 7 days
Question 19.
Ravish has three boxes whose total weight is
Kg. Box B weighs 
kg more than box A and box C weighs 
kg more than box B. Find the weight of box A.
Answer:
Total weight of three boxes is 
kg
Let the weight of box A is kg
Weight of box B = 
kg
Weight of box C = 
kg
According to the question:
LCM of 2 and 3 is 6
Therefore the weight of box A is 
kg
Question 20.
The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and the numerator by 2, we get the rational number 1/2. Find the rational number.
Answer:
Le the denominator is x
Numerator is x - 3
Fraction = 
= 
According to the question:
Numerator is increased by 2 and Denominator is increased by 5, then fraction is 1/2
On cross multiplication, we get
2(x - 1) = x + 52x - 2 = x + 5
2x - x = 2 + 5
x = 7
Therefore Denominator = 7
Numerator = x - 3 = 7 - 3 = 4
Therefore fraction = 4/7
Question 21.
In a rational number, twice the numerator is 2 more than the denominator If 3 is added to each, the numerator and the denominator. The niw fraction is 2/3. Find the original number.
Answer:
Le the numerator is
Denominator is 
Fraction = = 
According to the question:
Numerator and Denominator are increased by 3, then fraction is 
On cross multiplication, we get
Therefore numerator =7
Denominator = 
Therefore fraction = 
Question 22.
The distance between two stations is 340 km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater then that of the other by 5 km/hr. If the distance between the two trains after 2 hours of their start is 30 km, find the speed of each train.
Answer:
Let the speed of one train = km/hr
Speed of other train = 
km/hr
Distance 
Distance covered by one train in 2 hrs = 
km
Distance covered by other train in 2 hrs = 
km
Remaining distance between the train = 30 km
Therefore speed of one train = 75 km/hr
Speed of other train = 
km/hr
Question 23.
A steamer goes downstream from one point another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/hr, find the speed of the steamer in still water and the distance between the ports.
Answer:
Let the speed of steamer = x km/hr
Speed of stream = 1 km/hr
Downstream speed = (x + 1) km/hr
Upstream speed = (x – 1) km/hr
Distance = speed × time
⇒ 9 (x + 1) = 10 (x – 1)
9 x + 9 = 10 x – 10
x = 10 + 9 = 19 km/hr
Therefore speed of the steamer is 19 km/hr
Distance travelled = 9(x + 1) = 9 × 20 = 180 km.
Question 24.
Bhagwanti inherited Rs 12000.00. She invested part of it as 10% and the rest at 12%. Her annual income from these investements is Rs 1280.00 How much did she invest at each rate?
Answer:
Let one part is Rs
Other part is 
One part of investment = 
Other part of investment = 
Total investment = 1280
On cross multiplication, we get
Therefore one part is Rs 8000 and other part is Rs 4000
Question 25.
The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm2 more than that of the given rectangle. Find the length and breadth of the given rectangle.
Answer:
Let the breadth of the rectangle is meter
Length of the rectangle is 
meter
Area of the rectangle = length× breadth = 
m2
New length = 
New breadth = 
New area is 84 more than the pevious area:
Therefore length of the rectangle = 17m and breadth of the rectangle is 17m.
Question 26.
The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old as his father. What are their ages now?
Answer:
Let the age of Anup is x years
Let the age of Anup’s father is (100 - x) years
The age of Anuj = 
years
According to the question:
When Anup is as old as his father is now:
Then after (100 - x) years Anuj’s age = present age of his father (Anup) + 8
Present age of Anuj + 100 - 2x = Present age of Anup + 8
On cross multiplication, we get
Therefore age of Anup is 35 years, Age of Anup’s father = 100-35 = 65 years
The age of Anuj is = 
years
Question 27.
A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a begger waiting outside the shop. She spent half of what was left of what was left on a lunch and followed that up with a two rupee itp. She spent half of the remaining amount on a book and three rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?
Answer:
Let the amount available with lady is Rs
Amount spend for hankies and given to bagger = 
Remaining amount = 
= 
Expences for lunch 
Amount of tip = Rs 2
Amount remained after lunch = 
Amounts spend for books = 
Bus fare = Rs 3
Amount left = 
According to the question amount left = Re 1
On cross multiplication, we get
Therefore original amount with lady was Rs. 42