Ratio And Proportion

(a) From the question, the number of girls = 20

and, the number of boys = 15

Now,

Total number of students = Number of girls + Number of boys

= 20 + 15

= 35

Hence, the ratio of number of girls to boys

=

=

=

Thus the ratio of girls to boys is 4:3

(b) The strength of girls = 20

The strength of boys = 15

Now, Total number of students = Number of girls + Number of boys

= 20 + 15 = 35

Hence,

The ratio of the number of girls to the total number of students can be calculated as follows:

=

=

=

Thus, the ratio of number of girls to the total number of students is : 4: 7

(a) Here,

It is given in the question that:

Total number of students = 30

Number of students like to play football = 6

Also,

Number of students like to play cricket = 12

Now,

We can calculate the number of liking tennis as follows:

= Total number of students – (Number of students liking football + Number of students liking cricket)

= 30 – (6 + 12)

= 30 – 18

= 12

Hence,

Ratio of number of students liking football to the number of students liking tennis can be calculated as follows:

=

=

=

(b) We already know that,

Number of students liking cricket = 12

And,

Total number of students = 30

Hence,

Ratio of number of students liking cricket to the total number of students can be calculated as follows:

=

=

=

(a) We can observe from the given figure that,

Number of triangles = 3

Number of squares = 2

Number of circles = 2

Hence,

Total number of figures = 3 + 2 + 2

= 7

Now,

We can calculate the ratio of the number of triangles to the number of circles as follows:

=

=

(b) Here,

We know that:

Number of squares = 2

Hence,

We can calculate the ratio of the number of squares to the total number of figures as follows:

=

=

(c) The number of circles to all the figures inside the rectangle.

Here,

We know that:

Number of circles = 2

Hence,

We can calculate the ratio of the number of circles to the total number of figures as follows:

=

=

The ratio is 2:7.

We know that,

The speed of an object is the distance travelled by it in an hour.

Now,

It is given in the question that,

Distance travelled by Hamid in 1 hour = 9 km

Also,

Distance travelled by Akhtar in 1 hour = 12 km

Therefore,

Speed of Hamid = 9 km/h

Also,

Speed of Akhtar = 12 km/h

Hence,

We can calculate the ratio of speed of Hamid to the speed of Akhtar as follows:

=

=

=

We can calculate the ratios of the blank as follows:

= =

= × =

= × =

Hence,

5, 12 and 25 will come in those blanks respectively

Here,

We can clearly see that,

All these ratios are equivalent.

(a) We have to find the ratio of 81 to 108

⁼⁼

ratio of 81 to 108 is 3:4.

(b) We have to find the ratio of 98 to 63

⁼⁼

Ratio of 98 to 63 is 14:9

(c) We have to find the ratio of 33 km to 121 km

⁼⁼

Ratio of 33 km to 121 km is 3:11.

(d) We have to find the ratio of 30 minutes to 45 minutes.

^{= =}

Ratio of 30 min to 45 min is 2:3.

(a) We have,

30 minutes = =


0.5 hours

Therefore,

Required ratio =


As 1.5 = 0.5 × 3

=

=

(b) We have,

1.5 m = 1.5 × 100

= 150 cm

Therefore,

Required ratio =

=

(c) We have,

Rupee 1 = 100 paise

Therefore,

Require ratio =

=

=

(d) We have,

1 litre = 1000 ml

Also,

2l = 2000 ml

Therefore,

Required ratio =

=

=

=

Ratio is 1:4.

(a) It is given in the question that,

Money earned by Seema = Rs. 150000

Also,

Money saved by Seema = Rs. 50000

Therefore,

Money spent by Seema = Rs. 150000 – Rs. 50000

= Rs. 100000

Now,

Ratio of money earned to money saved =

=

(b) We have,

Money saved by Seema = Rs. 50000

Money spent by Seema = Rs. 100000

Hence,

Ratio of money saved to money spent =

=

Given in the question that,

Number of students in school = 3300

Number of teachers in school = 102

Therefore,

Ratio of number of teachers to the number of students =

=

=

Hence Ratio of teachers to students is 17:550

(a) It is given in the question that,

Total number of students = 4320

Number of girls = 2300

Therefore,

Required ratio =

=

=

Ratio is 115:216

(b) It is given in the question that,

Number of girls = 2300

Therefore,

Number of boys = 4320 – 2300

= 2020

Therefore,

Required ratio =

=

=

(c) We have,

Total number of students = 4320

Also,

Number of boys = 2020

Therefore,

Required ratio =

=

=

Ratio is 101:216

(a) It is given in the question that,

Total number of students = 1800

Number of students opted basketball = 750

Also,

Number of students opted cricket = 800

Therefore,

Number of students opted table tennis = Total students – (Number of students opted basketball + Number of students opted cricket)

= 1800 – (750 + 800)

= 1800 – 1550

= 250

Hence,

Required ratio =

=

=

(b) It is given in the question that,

Total number of students opting cricket = 800

Also,

Number of students opted basketball = 750

Required ratio =

=

(c) It is given in the question that,

Number of students opted basketball = 750

Also,

Total number of students = 1800

Therefore,

Required ratio =

=

=

The ratio is 5:12.

It is given in the question that,

Cost of dozen of pens = Rs. 180

Therefore,

Cost of 1 pen =

= Rs. 15

Also,

Cost of a ball pen =

= Rs. 7

Therefore,

Required ratio =

=

= 15:7

(i) Firstly,

It is given in the question that ratio of breadth and length of hall is 2: 5

Also, we have:

Length = 50 m

Therefore,

=

5 × breadth = 50 × 2 [By cross multiplying]

5 × breadth = 100

Hence,

Breadth =

= 20 m

(ii) In this part, we have

Breadth = 40 m

It is given in the question that ratio of breadth and length of hall is 2: 5

Therefore,

=

2 × Length = 5 × 40 [By cross multiplying]

2 × Length = 200

Hence,

Length =

= 100 m

In this question, we have

Terms of 3: 2 are 3 and 2

Therefore,

Sum of these terms = 3 + 2 = 5

Also,

Sheela will get of total pens and Sangeeta will get of total pens

Hence,

Number of pens with Sheela = × 20 = 12

Also,

Number of pens with Sangeeta = × 20 = 8

It is given in the question that,

Age of Shreya = 15 years

Also,

Age of Bhoomika = 12 years

Therefore,

Ratio of their ages = =

Hence, mother wants to divide Rs 36 in a ratio of 5: 4

From above ratios, we have

Terms of 5: 4 are 5 and 4

Therefore,

Sum of these terms = 5 + 4 = 9

Now,

Shreya will get of the total money and Bhoomika will get of that money

Hence,

Amount of money that Shreya will get = × 36 = 20

Also,

Amount of money that Bhoomika will get = × 36 = 16

Therefore,

Amount of money that Shreya get = Rs. 20

And,

Amount of money that Bhoomika get = Rs. 16

(a) It is given in the question that,

Present age of father = 42 years

Also,

Present age of son = 14 years

Therefore,

Required ratio =

=

=

(b) The ages 2 years ago:

Age of son = 12 years

Also,

Age of father = 42 – 2 = 40 years

Therefore,

Required ratio =

=

=

(c) The ages 10 years later:

Age of son = 24 years

Also,

Age of father after 10 years = 52 years

Therefore,

Required ratio =

=

=

(d) The ages 12 years ago:

Age of son = 14 – 12 = 2 years

Also,

Age of father = 30 years

Therefore,

Required ratio =

=

=

(a) In the given question,

We have to check if the given numbers are in proportion.

Now,

We know that,

A proportion happens when two ratios are forced to be equal to each other.

Thus,

And,

Therefore,

15 : 45 = 40 : 120

Hence,

We can clearly observe that,

The given numbers are in proportion.

(b) In the given question,

We have to check if the given numbers are in proportion.

Now,

We know that,

A proportion happens when two ratios are forced to be equal to each other.

Thus,

And,

Therefore,

33 : 121 ≠ 9 : 96

Hence,

We can clearly observe that,

The given numbers aren’t in proportion.

(c) In the given question,

We have to check if the given numbers are in proportion.

Now,

We know that,

A proportion happens when two ratios are forced to be equal to each other.

Thus,

And,

Therefore,

24 : 28 ≠ 36 : 48

Hence,

We can clearly observe that,

The given numbers are not in proportion.

(d) In the given question,

We have to check if the given numbers are in proportion.

Now,

We know that,

A proportion happens when two ratios are forced to be equal to each other.

Thus,

And,

Therefore,

32 : 48 ≠ 70 : 210

Hence,

We can clearly observe that,

The given numbers are not in proportion.

(e) In the given question,

We have to check if the given numbers are in proportion.

Now,

We know that,

A proportion happens when two ratios are forced to be equal to each other.

Thus,

And,

Therefore,

4 : 6 = 8 : 12

Hence,

We can clearly observe that,

The given numbers are in proportion.

(f) In the given question,

We have to check if the given numbers are in proportion.

Now,

We know that,

A proportion happens when two ratios are forced to be equal to each other.

Thus,

And,

Therefore,

33 : 44 = 75 : 100

Hence,

We can clearly observe that,

The given numbers are in proportion.

In the given question,

We have to check if the given statement is true.

To check it we will show if the ratio of terms are equal or not.

(a)16 : 24 : : 20 : 30

Now,

And,

Therefore,

16 : 24 : : 20 : 30

Hence,

The given statement is true.

(b) 21 : 6 : : 35 : 10

Now,

And,

Therefore, 21 : 6 : : 35 : 10

The given statement is true.

(c) 12 : 18 : : 28 : 12

Now,

And,

Here, 12 : 18 ≠ 28 : 12

Hence, the given statement is false.

(d) 8 : 9 : : 24 : 27

Now,

And,

Therefore,

8 : 9 = 24 : 27

The given statement is true.

(e) 5.2 : 3.9 : : 3 : 4

Now,

And,

Here,

5.2 : 3.9 ≠3 : 4

Hence,

The given statement is false.

(f) 0.9 : 0.36 : : 10 : 4

Now,

And,

Therefore,

0.9 : 36 = 10 : 4

Hence,

The given statement is true.

(a) In the given question,

We have to check if the given statement is true.

Now,

We can check this as follows,

And,

Therefore,

40 : 200 = 15 : 75

Hence,

We can clearly observe that,

The given statement is true.

(b) In the given question,

We have to check if the given statement is true.

Now,

We can check this as follows,

And,

Therefore,

7.5 : 15 = 5 : 10

Hence,

We can clearly observe that,

The given statement is true.

(c) In the given question,

We have to check if the given statement is true.

Now,

We can check this as follows,

And,

Therefore,

99 : 45 = 44 : 20

Hence,

We can clearly observe that,

The given statement is true.

(d) In the given question,

We have to check if the given statement is true.

Now,

We can check this as follows,

And,

Therefore,

32 : 64 = 6 : 12

Hence,

We can clearly observe that,

The given statement is true.

(e) In the given question,

We have to check if the given statement is true.

Now,

We can check this as follows,

And,

Therefore,

45 : 60 ≠ 12 : 15

Hence,

We can clearly observe that,

The given statement is false.

(a) At first,

25 cm = m

= 0.25

Now,

We can check this as follows,

And,

Therefore,

45 : 60 = 12 : 15

Hence,

We can clearly observe that,

They are in proportion.

Thus,

Middle terms are 1 m, Rs 40

And,

Extreme terms are 25 cm, Rs 160.

(b) At first,

We have to check if they are in proportion.

Now,

We can check this as follows,

And,

Therefore,

39:65 = 6 : 10

Hence,

We can clearly observe that,

They are in proportion.

Thus,

Middle terms are 65 l, 6 bottles

And,

Extreme terms are 39 l, 10 bottles.

(c) At first,

We have check if they are in proportion:

Now,

We can check this as follows,

And,

Therefore,

2 : 80 ≠ 25 : 625

Hence,

We can clearly observe that,

They are not in proportion.

(d) At first,

1l =

2.5l = 2500 ml

Now,

We can check this as follows,

And,

Therefore,

200: 2500 = 4 : 50

Hence,

We can clearly observe that,

They are in proportion.

Thus,

Middle terms are 2.5l, Rs 4

And,

Extreme terms are 200ml, Rs 50

It is given in the question that,

Cost of 7 m of cloth = Rs. 294

Cost of 1 m of cloth =

= Rs.42

Therefore,

Cost of 5 m of cloth = 5× Cost of 1 m cloth

= Rs. 5 × 42

= Rs. 210

It is given in the question that,

Money earned in 10 days = Rs. 1500

Therefore,

Money earned in 1 day = = Rs. 150

Hence,

Money earned in 30 days = 150 × 30 = Rs. 4500

It is given in the question that,

Measure of rain in 3 days = 276 mm

Therefore,

Measure of rain in 1 day = = 92 mm

Hence,

Measure of rain in 7 days = 92 × 7

= 644 mm

As,





= 64.4 cm

(a) It is given in the question that,

Cost of 5 kg wheat = Rs. 91.50

Therefore,

Cost of 1 kg wheat =

= Rs 18.3

Hence,

Cost of 8 kg wheat = 18.3 × 8

= Rs. 146.40

(b) It is given that,

Wheat purchased in Rs. 91.50 = 5 kg

Therefore,

Wheat purchased in Rs. 1 = kg

Hence,

Wheat purchased in Rs. 183 =





= 10 kg

It is given in the question that,

Temperature drop in 30 days = 15^oC

Therefore,

Temperature drop in 1 day = = ()^o C

Therefore,

Temperature drop in next 10 days = × 10 = 5^o C

Hence,

There will be a temperature drop of 5^o C in the next ten days.

It is given in the question that,

Rent for 3 months = Rs 7500

Therefore,

Rent for 1 month =

= Rs. 2500

Hence,

Rent for 12 months = 2500 × 12

= Rs. 30000

Thus, Shaina has to pay Rs. 30000 for a whole year.

It is given in the question that,

Number of bananas bought in Rs. 60 = 4 dozens

As 1 dozen = 12

= 4 × 12

= 48

Number of bananas bought in Rs. 1 =

Therefore,

Number of bananas bought in Rs. 12.50 = × 12.50

= 10 bananas

Hence, 10 bananas can be produced for Rs. 12.50

It is given in the question that,

Weight of 72 books = 9 kg

Therefore,

Weight of 1 book = (9/72) kg

=1/8 kg

Hence,

Weight of 40 books = × 40

= 5 kg

Thus, the weight of 40 such books is 5 kg.

It is given in the question that,

Diesel required for 594 km = 108 litres

Therefore,

Diesel required for 1 km =

= litre

Hence,

Diesel required for 1650 km = × 1650

= 300 litres

Therefore, 300 litres diesel will be required by the truck to cover a distance of 1650 km.

It is given in the question,

Raju purchased 10 pens for Rs. 150

Therefore,

Price of 1 pen =

= Rs. 15

It is also given that,

Manish purchased 7 pens for Rs. 84

Therefore,

Price of 1 pen =

= Rs. 12

Hence, Manish got the pens in cheaper rate

It is given in the question that,

Runs made by Anish in 6 overs = 42

Therefore,

Runs made by Anish in 1 over = = 7

It is also given that,

Runs made by Anup in 7 overs = 63

Therefore,

Runs made by Anup in 1 over = = 9

Hence,

It is clear from above that Anup made more runs per over.