Commercial Arithmetic
Class 8th Mathematics Part Ii Karnataka Board Solution
- In a school, 30% of students play chess, 60% play carrom and the rest play other…
- In a school function ₹ 360 remained after spending 82% of the money. How much…
- Akshay’s income is 20% less than that of Ajay. What percent is Ajay’s income…
- A daily wage employee spends 84% of his weekly earning. If he saves ₹ 384, find…
- A factory announces a bonus of 10% to its employees. If an employee gets ₹…
- Sonu bought a bicycle for ₹ 3,750 and spent ₹ 250 on its repairs. He sold it for…
- A shopkeeper purchases an article for ₹ 3,500 and pays transport charge of ₹…
- By selling a watch for ₹ 720, Ravi loses 10%. At what price should he sell it,…
- Hari bought two fans for ₹ 2,400 each. He sold one at a loss of 10% and the…
- A storekeeper sells a book at 15% gain. Had he sold it for 18 more, he would…
- The cost price of 12 pens is equal to selling price of 10 pens. Find the profit…
- An article marked ₹ 800 is sold for ₹ 704. Find the discount and discount…
- A dress is sold at ₹ 550 after allowing a discount of 12%. Find its marked…
- A shopkeeper buys a suit piece for ₹ 1,400 and marks it 60% above the cost…
- A dealer marks his goods 40% above the cost price and allows a discount of 10%.…
- A dealer is selling an article at a discount of 15%. Find: (i) the selling price…
- Sindhu sells her scooty for ₹ 28,000 through a broker. The rate of brokerage is…
- A share agent sells 2000 shares at ₹ 45 each and gets the commission at the rate…
- A person insures ₹ 26,000 through an insurance agent. If the agent gets ₹ 650 as…
- A selling agent gets 10,200 in a month. This includes his monthly salary of ₹…
- Find the simple interest on ₹ 2,500 for 4 years at 6 1/4 % per annum.…
- Find the simple interest on ₹ 3,500 at the rate of 2 1/2 % per annum for 165…
- In what period will ₹ 5,200 amounts to ₹ 7,384 at 12% per annum simple interest?…
- Ramya borrowed a loan from a bank for buying a computer. After 4 years she paid…
- A sum of money triples itself in 8 years. Find the rate of interest.…
- A person purchases the following items from a mall for which the sales tax is…
- A person buys electronic goods worth ₹ 10,000 for which the sales tax is 4% and…
- A trader purchases 70 Kg of tea at the rate of ₹ 200/Kg and another 30 kg at the…
- The principal that yields a simple interest of ₹ 1,280 at 16%per annum for 8 months…
- Nine percent of ₹ 700 is:A. ₹ 63 B. ₹ 630 C. ₹ 6.3 D. ₹ 0.63
- What per cent of 50 metres are 12 metres?A. 20% B. 60% C. 24% D. 32%…
- The number whose 8% is 12 is:A. 120 B. 150 C. 130 D. 140
- An article costing ₹ 600 is sold for ₹ 750. The gain percentage is:A. 20 B. 25 C. 30…
- By selling note book for ₹ 22 a shopkeeper gains 10%. The cost price of the book is:A.…
- The percentage of loss, when an article worth ₹ 10,000 wassold for ₹ 9,000 is:A. 10 B.…
- A radio marked 1000 is given away for ₹ 850. The discount is:A. ₹ 50 B. 100 C. 150 D.…
- A book marked ₹ 250 was sold for ₹ 200 after discount. The percentage of discount…
- The marked price of an article is ₹ 200. If 15% of discount is allowed on it, its…
- One sells his bike through a broker by paying ₹ 200 brokerage.The rate of brokerage is…
- The brokerage amount for a deal of ₹25,000 at 2% rate of commission is:A. ₹ 500 B. ₹…
- If ₹ 1,600 is the commission at 8% for goods sold through abroker, the selling price…
- The simple interest on ₹ 5,000 at 2% per month for 3 months is:A. ₹ 100 B. ₹ 200 C. ₹…
- The time in which simple interest on a certain sum be 0.15times the principal at 10%…
- A time interval of 3 minutes and 20 seconds is wrongly measured at 3 minutes and 25…
- Hari reads 22% of the pages of a book on the first day, 53% on the second day and 15%…
- If 55% of students in a school are girls and the number of boys is 270, find the number…
- By selling an article for ₹ 920, a shopkeeper gains15%. Find the cost price of the…
- Amit sells a watch at a 20% gain. Had he sold it for ₹ 36 more, he would have gained…
- On selling apples at 40 per Kg, a vendor incurs 10% loss. If he incurs a total loss of…
- A dealer allows a discount of 20% and still gains 20%. Find the marked price of an…
- A shopkeeper buys an article for ₹ 600 and marks 25% above the cost price. Find (i) the…
- A retailer purchases goods worth ₹ 33,600 and gets a discount of 14% from a whole…
- An old car was disposed through a broker for ₹ 42,000. If the broker age is 2 1/2%,…
- A milk-man sells 20 litres of milk every day at ₹ 22. He receives a commission of 4%…
- A bike was sold for ₹ 48,000 and a commission of ₹ 8,640 was received by the dealer.…
- In how many years will a sum of money becomes three times at the rate of interest 10%…
- In what time will the simple interest on a certain sum be 0.24 times the principal at…
- Find the amount of ₹ 30,000 from 15th January 2010 to 10th August 2010 at 12% per…
- A person purchases electronic items worth ₹ 2,50,000. The shopkeeper charges him a…
Exercise 9.1
Question 1.In a school, 30% of students play chess, 60% play carrom and the rest play other games. If the total number of students in the school is 900, find the exact number of students who play each game.
Answer:
Total number of students = 900
No. of students who play chess = 30% of total no. of students
= 30% x 900
= 270
No. of students who play carrom = 30% of total no. of students
= 60% × 900
= 540
No. of students who play other games = 100%-(60%+30%) of
total students
= 10% x 900
=90
Question 2.
In a school function ₹ 360 remained after spending 82% of the money. How much money was there in the beginning? Verify your answer.
Answer:
Let the money in beginning was x
Percentage (%) of money spent = 82%
⇒ Percentage (%) of money remaining = 18%
Amount remaining = 360
⇒ 18% of x = 360
Verification: 82% of 2000 
= 1640
And 2000-1640 = Rs.360,
which was our remaining 18 %
Question 3.
Akshay’s income is 20% less than that of Ajay. What percent is Ajay’s income more than that of Akshay?
Answer:
Let the income of ajay be x
Aksahy’s income = (100-20)% of Ajay’s income
= 80% of x
= 0.80x
Then, percentage of = 
ajay’s income more than that of akshay
= 25%
è Tip: For better understanding, you can imagine Ajay’s income be 100.
Then akshay’s income would become 80. So % of ajay’s income greater than that of akshay will be 100-80 = 20
20 is 25% of 80 (akshay’s income)
Don’t write this in your exam.
Question 4.
A daily wage employee spends 84% of his weekly earning. If he saves ₹ 384, find his weekly earning.
Answer:
Let the weekly earning be x
Percentage (%) of money spent = 84%
⇒ Percentage (%) of money remaining = 16%
Amount saved =384
⇒ 16% of x = 384
So, weekly earning is 2400
Question 5.
A factory announces a bonus of 10% to its employees. If an employee gets ₹ 10,780, find his actual salary.
Answer:
Let the salary be x
Percentage (%) of bonus = 10%
⇒ Amount of bonus = 10% of x
Total salary received = 10% of x + x = 10,780
= 1.1 x
⇒ 1.1 x = 10,780
X= 9800
So, salary is 9800
Exercise 9.2
Question 1.Sonu bought a bicycle for ₹ 3,750 and spent ₹ 250 on its repairs. He sold it for ₹ 4,400. Find his loss or profit percentage.
Answer:
CP of cycle = ₹ 3,750
Overhead expenses = ₹ 250
Effective CP = CP of cycle + Overhead expenses
= Rs. 4,000
SP of cycle = Rs. 4,400
Profit = SP – Effective CP
= 4400-4000
= 400
Profit % 
= 
= 10%
So, Profit is Rs.400 & profit % = 10%
Question 2.
A shopkeeper purchases an article for ₹ 3,500 and pays transport charge of ₹ 100. He incurred a loss of 12% in selling this. Find the selling price of the article.
Answer:
CP of article = ₹ 3500
Overhead expenses = ₹ 100
Effective CP = CP + Overhead expenses
= Rs. 3,600
Loss % 
= 12%
⇒ 
Loss = 12 x 36
= Rs. 432
SP = CP- Loss
= 3600-432
= Rs. 3168
Question 3.
By selling a watch for ₹ 720, Ravi loses 10%. At what price should he sell it, in order to gain 15%?
Answer:
Let the CP of watch be x
SP of watch = ₹ 720
Loss = 10% of CP
Also, Loss = CP – SP
⇒ 10% of x = x – 720
CP of watch is Rs.800
Now for profit of 15%
Profit %
Profit = 120
SP of watch = CP + profit
= 800+120
= 920
∴ Ravi should sell watch at Rs.920 to gain 15%.
Question 4.
Hari bought two fans for ₹ 2,400 each. He sold one at a loss of 10% and the other at a profit of 15%. Find the selling price of each fan and find also the total profit or loss.
Answer:
CP of a fan = ₹ 2,400
He sold 1st fan at Loss of 10%
SP of 1st fan = CP – 10% of CP
⇒ SP of 1st fan = 2160
He sold another fan at profit of 15%
SP of 2nd fan = CP + 15% of CP
⇒ SP of 2nd fan = 2760
Overall Profit/Loss = SP of both fans – CP of both fans
= (2760+2160)-(2400+2400)
= 120
∴ He made an overall profit of Rs.120
Question 5.
A storekeeper sells a book at 15% gain. Had he sold it for 18 more, he would have gained 18%. Find the cost price of the book.
Answer:
Let the CP of book be x
1st SP = SP at Profit of 15%.
= 0.15x
2nd SP = SP at Profit of 18%
= 0.18x
Also, 2nd SP = 1st SP + 18
⇒ 0.18x = 0.15x + 18
⇒ 0.03x = 18
⇒ x = 600
∴ CP of book is Rs.600
Question 6.
The cost price of 12 pens is equal to selling price of 10 pens. Find the profit percentage.
Answer:
Let the CP of pen be x
CP of 12 pens = 12x
SP of 10 pens = 12x
SP of 1 pen 
= 1.2x
Profit = SP – CP
= 1.2x - x
= 0.2x
Profit %
∴ Profit percentage of pen is 20%.
Exercise 9.3
Question 1.An article marked ₹ 800 is sold for ₹ 704. Find the discount and discount percent.
Answer:
Marked price = 800
Selling price = 704
Discount = 800-704
= 96
Discount % 
∴ Discount is Rs.96 and discount percentage 12%.
Question 2.
A dress is sold at ₹ 550 after allowing a discount of 12%. Find its marked price.
Answer:
Let Marked price be x
Selling price = 550
Discount = x-550
= 96
Discount % 
∴ Marked price is Rs.625.
Question 3.
A shopkeeper buys a suit piece for ₹ 1,400 and marks it 60% above the cost price. He allows a discount of 15% on it. Find the marked price of the suit piece and also the discount given.
Answer:
CP of suit = 1,400
Marked price = 60% of CP + CP
= 
= 2240
Discount % = 15%
Discount %
Discount = Rs.336
∴ Marked price is Rs.2240, discount given is Rs.336 and marked price after discount Rs.1904.
Question 4.
A dealer marks his goods 40% above the cost price and allows a discount of 10%. Find the profit percent.
Answer:
Let CP of goods be x
Marked price = 40% of CP + CP
= 
= 1.40x
Discount % = 10%
Discount %
Discount = 0.14x
SP = Marked price - Discount
= 1.40x - 0.14x
= 1.26x
Profit = SP – CP
= 1.26x-x
= 0.26x
Profit % 
∴ Profit % is 26%.
Question 5.
A dealer is selling an article at a discount of 15%. Find:
(i) the selling price if the marked price is ₹ 500;
(ii) the cost price if he makes 25% profit.
Answer:
(i) Marked price = 500
Discount % = 15%
Discount %
SP = 500 - 75
= 425
∴ Selling price is Rs.425
(ii) let the CP be x
Profit %
Profit = SP – CP
0.25x = 425 – x
1.25x = 425
x = 
x = 340
∴ Cost price is Rs.340.
Exercise 9.4
Question 1.Sindhu sells her scooty for ₹ 28,000 through a broker. The rate of brokerage is 2.5 %. Find the commission that the agent gets and the net amount Sindhu gets.
Answer:
Let net amount sindhu gets be x
Brokerage rate = 2.5%
Brokerage charges = 
Selling price of scooty = 28,000
Selling Price = amount sindhu gets + brokerage charges
= x+0.025x
1.025x = 28,000
x = 
x = 27,300 (rounded off, actual value 27317.07)
∴ Money sindhu gets = Rs.27,300
The commission that the agent gets = 28000-27300
= Rs.700
Question 2.
A share agent sells 2000 shares at ₹ 45 each and gets the commission at the rate of 1.5%. Find the amount the agent gets.
Answer:
Price of each share = Rs.45
Commission rate per share = 1.5%
Commission charges per share = 
= Rs 0.675
Total commission = 2000 x per share commission
= 2000 x 0.675
= Rs1350
∴ The commission agent gets = Rs1350
Question 3.
A person insures ₹ 26,000 through an insurance agent. If the agent gets ₹ 650 as the commission, find the rate of commission.
Answer:
Amount person insures = Rs.26,000
Amount agent gets (Commission) = Rs.650
% of commission = 
= 2.5%
∴ Percentage of commission agent gets = 2.5%
Question 4.
A selling agent gets 10,200 in a month. This includes his monthly salary of ₹ 6000 and 6% commission for the sales. Find the value of goods he sold.
Answer:
Salary = Rs.6000
Total money he got = Rs.10,200
Money as commission for sales = 10200-6000
= 4200
Since rate of commission is 6%. So, money he got as commission is 6% the value of goods he sold.
⇒ 6% of value of goods = 4200
⇒ value of goods 
⇒ value of goods = 70000
∴ Value of goods he sold is Rs70000
Exercise 9.5
Question 1.Find the simple interest on ₹ 2,500 for 4 years at 
% per annum.
Answer:
Simple interest (SI) 
Here,
Principal amount (P) = Rs.2500
Time (T) = 4 years
Rate of interest =
%
= 6.25 %
SI = 
= 625
∴ Simple interest = Rs625
Question 2.
Find the simple interest on ₹ 3,500 at the rate of 
% per annum for 165 days.
Answer:
Simple interest (SI)
Here,
Principal amount (P) = Rs.3500
Time (T) = 165 days = 
Rate of interest =
%
= 2.5 %
SI = 
= 39.55
∴ Simple interest = Rs39.55
Question 3.
In what period will ₹ 5,200 amounts to ₹ 7,384 at 12% per annum simple interest?
Answer:
Simple interest (SI)
Here,
SI = 7384-5200
= 2184
Principal amount (P) = Rs.5200
Rate of interest = 12%
Time (T) = 
= 3.5 years
∴ Time period = 3.5 years
Question 4.
Ramya borrowed a loan from a bank for buying a computer. After 4 years she paid ₹ 26,640 and settled the accounts. If the rate of interest is 12% per annum, what was the sum she borrowed?
Answer:
Simple interest (SI)
Here,
Loan amount borrowed be P
SI = 26640-P
= 2184
Rate of interest = 12%
Time (T) = 4
Loan amount P = 
∴ Amount Ramaya borrowed =Rs 18,000
Question 5.
A sum of money triples itself in 8 years. Find the rate of interest.
Answer:
Simple interest (SI)
Here,
Let Principal amount (P) = x
Time (T) = 8 years
Amount at end of 8 years = 3x
SI = 3x-x
= 2x
Rate (R) = 
= 25%
∴ Rate of interest = 25%.
Exercise 9.6
Question 1.A person purchases the following items from a mall for which the sales tax is mentioned against:
(a) Stationery materials for ₹ 250 and sales tax of 4% there on;
(b) Electronic goods worth ₹ 2,580 and sales tax of 10% there on;
(c) Groceries worth ₹ 1,200 on which sales tax of 3% is levied;
(d) Medicines worth ₹ 200 with sales tax of 6%. Find the bill amount for each item.
Answer:
(a) Price of goods = 250
Tax = 4%
Tax amount = 
= 10
Bill amount = Price of goods + tax amount
= 250+10
= 260
(b) Price of goods = 2580
Tax = 10%
Tax amount = 
= 258
Bill amount = Price of goods + tax amount
= 2580+258
= 2838
(c) Price of goods = 1200
Tax = 3%
Tax amount = 
= 36
Bill amount = Price of goods + tax amount
= 1200+36
= 1236
(d) Price of goods = 200
Tax = 6%
Tax amount = 
= 12
Bill amount = Price of goods + tax amount
= 200+12
= 212
Question 2.
A person buys electronic goods worth ₹ 10,000 for which the sales tax is 4% and other material worth ₹ 15,000 for which the sales tax is 6%. He manufactures a gadget using all these and sells it at 15% profit. What is his selling price?
Answer:
Price of electronic goods = 10,000
Tax = 4%
Tax amount = 
= 400
Net amount of = Price of goods + tax amount
electronic goods
= 10000+400
= 10400
Price of other materials = 15,000
Tax = 6%
Tax amount = 
= 900
Net amount of = Price of goods + tax amount
Other materials
= 15000+900
= 15900
Net amount for input = 10400+15900
material of gadget
= 26300
Profit %
∴ SP = CP + profit
= 26300+3945
= Rs30245
Question 3.
A trader purchases 70 Kg of tea at the rate of ₹ 200/Kg and another 30 kg at the rate of ₹ 250/Kg. He pays a sales tax of 4% on the transaction. He mixes both of them and sells the product at the rate of ₹ 240/Kg. What is the percentage gain or loss? (find approximate value)
Answer:
Price of 1st type tea = 200/kg
Quantity = 70 kg
Amount = 200 x 70
= 14000
Price of 2nd type tea = 250/kg
Quantity = 30 kg
Amount = 250 x 30
= 7500
Total amount = 7500+14000
= 21500
Tax = 4%
Tax amount = 
= 860
Net amount for tea = total amount + tax
purchase (CP)
= 21500+860
= 22360
Total quantity for sale = 100 kg
Rate of selling = 240/kg
Total amount of sale (SP) = 240 x 100
= 24000
Overall Profit/Loss = SP– CP
= 24000-22360
Profit = 1640
Profit %
= 7.33%
∴ Profit % is 7.33 %
Additional Problems 9
Question 1.The principal that yields a simple interest of ₹ 1,280 at 16%per annum for 8 months is:
A. ₹ 10,000
B. ₹ 12,000
C. ₹ 12,800
D. 14,000
Answer:
Given: Rate = 16% per annum, Simple Interest = ₹ 1280,
⇒ P = ₹ 12,000
Question 2.
Nine percent of ₹ 700 is:
A. ₹ 63
B. ₹ 630
C. ₹ 6.3
D. ₹ 0.63
Answer:
Nine percent of ₹ 700 =
Question 3.
What per cent of 50 metres are 12 metres?
A. 20%
B. 60%
C. 24%
D. 32%
Answer:
Let the required percentage be x%.
⇒ x = 12 × 2 = 24%
Question 4.
The number whose 8% is 12 is:
A. 120
B. 150
C. 130
D. 140
Answer:
Let the required number be x.
⇒ x = 150
Question 5.
An article costing ₹ 600 is sold for ₹ 750. The gain percentage is:
A. 20
B. 25
C. 30
D. 35
Answer:
Given CP = ₹ 600 and SP = ₹ 750
Gain = SP – CP = ₹ 750 - ₹ 600 = ₹ 150
⇒
Question 6.
By selling note book for ₹ 22 a shopkeeper gains 10%. The cost price of the book is:
A. 18
B. 30
C. 20
D. 22
Answer:
Given SP = ₹ 22 and gain = 10%
⇒
⇒ CP = 10 × Gain
Gain = SP – CP
⇒ SP = Gain + CP
⇒ 22 = Gain + 10Gain
⇒ 22 = 11 Gain
⇒ Gain =₹ 2
So, CP = 10 × Gain =₹ 20
Question 7.
The percentage of loss, when an article worth ₹ 10,000 wassold for ₹ 9,000 is:
A. 10
B. 20
C. 15
D. 25
Answer:
Given CP = ₹ 10,000 and SP = ₹9,000
Loss = CP – SP = ₹ 10000 - ₹ 9000 = ₹ 1000
Loss Percentage =
⇒
oss Percentage =
Question 8.
A radio marked 1000 is given away for ₹ 850. The discount is:
A. ₹ 50
B. 100
C. 150
D. 200
Answer:
Given MP = ₹1000 and SP = ₹ 850
Discount = MP – SP = ₹1000 - ₹ 850 = ₹ 150
Question 9.
A book marked ₹ 250 was sold for ₹ 200 after discount. The percentage of discount is:
A. 10
B. 30
C. 20
D. 25
Answer:
Given MP = ₹250 and SP = ₹ 200
Discount = MP – SP = ₹250 - ₹ 200 = ₹ 50
Discount Percentage =
⇒Discount Percentage = 
Question 10.
The marked price of an article is ₹ 200. If 15% of discount is allowed on it, its selling price is:
A. ₹ 185
B. ₹ 170
C. ₹ 215
D. ₹ 175
Answer:
Given MP = ₹200 and Discount % = 15%
⇒
⇒ Discount = ₹30
Discount = MP – SP
⇒ SP = MP – Discount
⇒ SP = ₹200 - ₹ 30 = ₹ 170
Question 11.
One sells his bike through a broker by paying ₹ 200 brokerage.The rate of brokerage is 2%. The selling price of the bike is:
A. ₹ 12,000
B. ₹ 10,000
C. ₹ 14,000
D. ₹ 12,500
Answer:
Given that brokerage = ₹200
Rate of brokerage = 2%
Let the SP be ₹ x
Then
⇒
⇒ SP = ₹ 10000
Question 12.
The brokerage amount for a deal of ₹25,000 at 2% rate of commission is:
A. ₹ 500
B. ₹ 250
C. ₹ 5,000
D. ₹ 2,500
Answer:
Given that SP = ₹25,000
Rate of brokerage = 2%
Then
⇒
⇒ Brokerage Amount = ₹ 500
Question 13.
If ₹ 1,600 is the commission at 8% for goods sold through abroker, the selling price of the goods is:
A. ₹ 18,000
B. ₹ 20,000
C. ₹ 22,000
D. ₹ 24,000
Answer:
Given that brokerage = ₹1600
Rate of brokerage = 8%
Let the SP be ₹ x
Then
⇒
⇒ SP = ₹ 20000
Question 14.
The simple interest on ₹ 5,000 at 2% per month for 3 months is:
A. ₹ 100
B. ₹ 200
C. ₹ 300
D. ₹ 400
Answer:
Given: Principle = ₹ 5,000, time = 3 months, Rate = 2% per month
Question 15.
The time in which simple interest on a certain sum be 0.15times the principal at 10% per annum is:
A. 1.5 years
B. 1 year
C. 2 years
D. 2.5 years
Answer:
Given: Let Principle be ₹P, Rate = 10% per annum, Simple Interest = ₹ 0.15 P
⇒ t = 1.5 years
Question 16.
A time interval of 3 minutes and 20 seconds is wrongly measured at 3 minutes and 25 seconds. What is the percentage error?
Answer:
Given: Actual Value = 3 minutes and 20 seconds = 200 seconds and Observed Value = 3 minutes and 25 seconds = 205 seconds
Error = Observed Value – Actual Value
Error= 5 seconds
Question 17.
Hari reads 22% of the pages of a book on the first day, 53% on the second day and 15% on the third day. If the number of pages remaining to be read is 30, find the total number of pages in the book.
Answer:
Given: % of pages read on first day = 22%
% of pages read on second day = 53%
% of pages read on third day = 15%
Total pages read = (22 + 53 + 15)% = 90%
Pages left to read = 10 %
According to the question,
10% of pages = 30
⇒ 100% of pages = 300
Hence, total pages in the book = 300
Question 18.
If 55% of students in a school are girls and the number of boys is 270, find the number of girls in the school.
Answer:
Given: %age of girls in the school = 55%
Number of boys in the school = 270
⇒ 45% of students in the school are boys.
Let total students be x
According to the question,
45% of x = 270
⇒ x = 600
Number of girls = 600 – 270 = 330
Question 19.
By selling an article for ₹ 920, a shopkeeper gains15%. Find the cost price of the article.
Answer:
Given: SP = ₹ 920, gain = 15%
⇒
Gain = SP – CP
⇒ SP = Gain + CP
⇒ Gain = ₹ 120
So, CP = SP - Gain =₹ 920 - ₹120 = ₹ 800
Question 20.
Amit sells a watch at a 20% gain. Had he sold it for ₹ 36 more, he would have gained 23%. Find the cost price of the watch.
Answer:
Given: Gain = 20%
If SP is increased by ₹ 36, gain = 23%
By an increase of ₹ 36, gain increases by 3%
⇒
⇒ CP = ₹ 1200
Question 21.
On selling apples at 40 per Kg, a vendor incurs 10% loss. If he incurs a total loss of ₹ 120, calculate the quantity (in Kg) of apples he sold.
Answer:
Given: SP = ₹40 per kg, total loss =₹120
Loss% = 10
Let the total quantity be x kg
CP = SP + Loss
⇒ CP = 40x + 120..(1)
⇒
⇒ CP = ₹ 1200
Putting in (1),
⇒ 40x + 120 = 1200
⇒ 40x = 1080
⇒ x = 27
Total quantity = 27 kg
Question 22.
A dealer allows a discount of 20% and still gains 20%. Find the marked price of an article which costs the dealer ₹ 720.
Answer:
Given: Discount % = 20%, Gain% = 20%, CP = ₹720
⇒ Gain =₹ 144
SP = CP + Gain
⇒ SP = 720 + 144 = ₹864
⇒
⇒ MP = 5 × Discount
Also, Discount = MP – SP
⇒ MP – Discount = SP
⇒ 5 × Discount - Discount = ₹ 864
⇒ 4 × Discount = ₹ 864
⇒ Discount = ₹ 216
MP = 5 × Discount = 5 × 216 = ₹1080
Question 23.
A shopkeeper buys an article for ₹ 600 and marks 25% above the cost price. Find (i) the selling price if he sells the article at 10% discount; (ii) the percentage of discount if it is sold for ₹ 690.
Answer:
(i) Given: CP = ₹ 600, MP = 125% of CP, Discount = 10%
⇒ Discount = ₹ 75
SP = MP – Discount = 750 – 75 = ₹ 675
(ii) Given: CP = ₹ 600, MP = 125% of CP, SP =₹ 690
Discount = MP – SP
⇒ Discount = ₹ 750 - ₹ 690= ₹60
Question 24.
A retailer purchases goods worth ₹ 33,600 and gets a discount of 14% from a whole seller. For paying in cash, the whole seller gives an additional discount of 1.5% on the amount to be paid after the first discount. What is the net amount the retailer has to pay?
Answer:
Given: CP =₹ 33,600, First Discount = 14%, Second Discount =1.5%
MP (after first discount)=
SP (after additional discount)=
Question 25.
An old car was disposed through a broker for ₹ 42,000. If the broker age is 2 1/2%, find the amount the owner gets.
Answer:
Given that SP = ₹42,000
Rate of brokerage = 2.5%
Then
⇒
⇒ Brokerage Amount = ₹ 1050
Amount the owner gets = ₹42,000 - ₹1050 = ₹41050
Question 26.
A milk-man sells 20 litres of milk every day at ₹ 22. He receives a commission of 4% for every litre. Find the total commission he receives in a month of 30 days.
Answer:
Given: Total milk sold per day =20 litres, SP of 1-litre milk = ₹22
The rate of brokerage = 4%
Then
⇒ Brokerage Amount =
⇒ Brokerage Amount = ₹ 0.88
Total commission of a day = ₹0.88 × 20 = ₹17.60
Total commission of a month =₹17.60 × 30 = ₹528.00
Question 27.
A bike was sold for ₹ 48,000 and a commission of ₹ 8,640 was received by the dealer. Find the rate of commission.
Answer:
Given: SP = ₹48,000, Brokerage amount =₹ 8,640
Then
⇒
⇒ Brokerage Rate = 18%
Question 28.
In how many years will a sum of money becomes three times at the rate of interest 10% per annum?
Answer:
Given: Let Principle be ₹ P, Rate = 10% per annum, Amount = ₹ 3P
Simple Interest =Amount – Principle
Simple Interest = 3P – P = 2P
⇒ t = 20 years
Question 29.
In what time will the simple interest on a certain sum be 0.24 times the principal at 12% per annum?
Answer:
Given: Let Principle be ₹ P, Rate = 12% per annum, Simple Interest =0.24P
⇒ t = 2 years
Question 30.
Find the amount of ₹ 30,000 from 15th January 2010 to 10th August 2010 at 12% per annum.
Answer:
Given: Principle = ₹ 30,000, Rate = 12% per annum, Time = 208 days
Simple Interest 
⇒ Simple Interest 
⇒ Simple Interest =₹2051.507
Amount =Principle + Interest
Amount =30,000 + ₹2051.507=₹32,051.507
Question 31.
A person purchases electronic items worth ₹ 2,50,000. The shopkeeper charges him a sales tax of 21% instead of 12%. The consumer does not realise that he has overpaid. But after some time he finds that he has paid excess and asks the shopkeeper to return the excess money. The shopkeeper refuses and the consumer moves the consumer court. The court with due hearing orders the shopkeeper to pay the consumer the excess money paid by the way of sales tax, with an interest of 12% per annum. If the whole deliberation takes 8 months, what is the money that the consumer gets back?
Answer:
Given: Taxable Amount = ₹ 2,50,000, Actual sales tax = 12%, Charged sales tax = 21%
Excess amount charged = 9% of 2,50,000
⇒ Excess amount charged =
Now, for interest:
P = ₹ 22500, R = 12%per annum, time = 8 months
Simple Interest =
Interest on Excess Amount =
Amount Received by consumer = ₹22500 + ₹1800 = ₹24300