Exercise 12.1

1. There are 20 girls and 15 boys in a class.

(a) What is the ratio of number of girls to the number of boys?

Instructions

(b) What is the ratio of number of girls to the total number of students in the class?

2. Out of 30 students in a class, 6 like football,12 like cricket and remaining like tennis. Find the ratio.

(a) Number of students liking football to number of students liking tennis.

Instructions

(b) Number of students liking cricket to total number of students.

3. See the figure and find the ratio.

(a) Number of triangles to the number of circles inside the rectangle.

Number of triangles = , Number of circles =

Ratio = Number of trianglesNumber of circles =

Thus, the required ratio is 3 : 2.

(b) Number of squares to all the figures inside the rectangle.

Number of squares = , Number of all figures =

Ratio = Number of squaresNumber of all figures =

Thus, the required ratio is 2 : 7.

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

Number of circles = , Number of all figures =

Ratio = Number of circlesNumber of all figures =

Thus, the required ratio is 2 : 7.

4. Distances travelled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the ratio of speed of Hamid to the speed of Akhtar.

Distance travelled by Hamid = km.

Distance travelled by Akhtar = km.

Speed of Hamid = km per hour

Speed of Akhtar = km per hour

Akhtar = Speed of HamidSpeed of Akhtar = = :

Thus, the required ratio is 3 : 4.

5. Fill in the following blanks:

1518 = /6 = 10/ = /30

Are these equivalent ratios? YesNo

6. Find the ratio of the following :

(a) 81 to 108

Ratio = 81108

Find the greatest common divisor (GCD) of 81 and 108, which is

Now simplify : 81108 = 81÷27108÷27 = 3443

Thus, the ratio of 81 to 108 is 3:4.

(b)98 to 63

Ratio = 9863

Find the greatest common divisor (GCD) of 98 and 63, which is

Now simplify : 9863 = 98÷763÷7 = 149145

Thus, the ratio of 98 to 63 is 14:9.

(c) 33 km to 121 km

Ratio = 33121

Find the greatest common divisor (GCD) of 33 and 121, which is

Now simplify : 33121 = 33÷11121÷11 = 311113

Thus, the ratio of 33 to 121 is 3:11.

(d) 30 minutes to 45 minutes

Ratio = 3045

Find the greatest common divisor (GCD) of 30 and 45, which is

Now simplify : 3045 = 30÷1545÷15 = 2342

Thus, the ratio of 30 to 45 is 2:3.

7. Find the ratio of the following:

(a) 30 minutes to 1.5 hours

We convert hours into minutes: 1.5 hours = 1.5 × mintutes.

= 1510 × = minutes

So, Ratio = 30minutes90minutes =

Required Ratio = 1 : 33 : 1

(b) 40 cm to 1.5 m

We convert m into cm 1.5 m = 1.5 × m

= 1510 × 100 = cm

Ratio = 40cm150cm =

Required Ratio = 4 : 1515 : 4

(c) 55 paise to ₹ 1

We convert Rs into paise Rs 1 = 1 × = paise

So, Ratio = 55paise100paise =

Required Ratio =11 : 2020 : 11

(d) 500 mL to 2 litres

We convert litre into ml 2 liters = 2 × ml = ml

So, Ratio = 500ml2000ml =

Required Ratio = 1 : 44 : 1

8. In a year, Seema earns ₹ 1,50,000 and saves ₹ 50,000. Find the ratio of

(a) Money that Seema earns to the money she saves.

Ratio = Seema earnsSeema saving = 15000050000 = = 3 : 11 : 3

(b) Money that she saves to the money she spends.

The money she spends = 1,50,000 - 50,000 = 1,00,00010,000

Ratio = Seema savingSeema spends = 50000100000 = = 1 : 22 : 1

9. There are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.

Number of teachers =

Number of students =

Ratio = Number of techersNumber of students =

The Greatest common divisor of 102 and 3300 is

So, dividing both by 6: 102÷63300÷6 =

Thus, the simplified ratio of the number of teachers to the number of students is 17 : 550500 : 17.

10. In a college, out of 4320 students, 2300 are girls. Find the ratio.

(a) Number of girls to the total number of students.

Ratio = Number of girlsTotal number of students = 2300432043202300 =

Required ratio =

(b) Number of boys to the number of girls.

Total number of students =

Number of girls =

Number of boys = Total number of students - Number of girls = 4320 - 2300 =

Ratio = Number of boysNumber of girls = 20202300 =

Required ratio =

(c) Number of boys to the total number of students.

Ratio = Number of boysTotal number of students = 20204320 =

Required ratio =

11. Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio.

Total number of students =

Number of students who opted for basketball =

Number of students who opted for cricket =

Number of students who opted for table tennis = Total number of students - Number of students who opted for basketball - Number of students who opted for cricket = - - =

(a) Number of students who opted basketball to the number of students who opted table tennis.

Ratio = Number of students who opted for basketballNumber of students who opted for table tennis

= 750250250800 =

(b) Number of students who opted cricket to the number of students opting basketball.

Ratio = Number of students who opted for cricketNumber of students who opted for basketball

= 800750750250 =

(c) Number of students who opted basketball to the total number of students.

Ratio = Number of students who opted for basketballTotal number of students

= 75018001800800 =

12. Cost of a dozen pens is ₹ 180 and cost of 8 ball pens is ₹ 56. Find the ratio of the cost of a pen to the cost of a ball pen.

Cost of dozen pens ( pens) = Rs 180

Cost of 1 pen = 18012 = Rs

Cost of 8 ball pens = Rs

Cost of 1 ball pen = 568 = Rs

Ratio = Cost of 1 penCost of 1 ball pen = (fraction form)

= 15:77:15 (ratio form)

13. Consider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the following table that shows some possible breadths and lengths of the hall.

Solution :

Given breadth and length = : (or) (fraction form)

We can express the length in terms of breadth or vice versa.

1. Breadth = 10 meters

Length = 5225 × = meters

2. Breadth = 40 meters

Length = 5225 × = meters

3. Length = 50 meters

Breadth = 2552 × = meters

14. Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.

Solution :

The ratio of dividing pens between Sheela and Sangeeta =

Now, let the total number of pens be (3 + 2) x =

5x = => x =

The total number of pens with Sheela = 3x => 3 × =

The total number of pens with Sangeeta = 2x => 2 × =

Therefore, Sheela gets 12 pens and Sangeeta gets 8 pens.

15. Mother wants to divide ₹ 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get.

Solution :

Total money = ₹

Age of Shreya = years

Age of Bhoomika = years

The greatest common divisor(GCD) for 15 and 12 is

Ratio = 153 : 123 =

Sum of parts in the ratio is 5 + 4 = parts

Amount received by Sherya's share = 5949 × = Rs

Amount received by Bhoomika's share = 4959 × = Rs

Therefore, Shreya and Bhoomika will get ₹ 20 and ₹ 16 respectively.

16. Present age of father is 42 years and that of his son is 14 years. Find the ratio.

(a) Present age of father to the present age of son.

Present age of father = years

Present age of son = years

So, Ratio = Present age of fatherPresent age of son = 42141442 =

Ratio =

(b) Age of the father to the age of son, when son was 12 years old.

Age of father =

2 years ago father age will be = 42 - 2 =

Age of son =

So, Ratio = Age of fatherAge of son = 40121240 =

Ratio =

(c) Age of father after 10 years to the age of son after 10 years.

Age of father after 10 years = Present age of father + 10

= + 10 = years

Age of son after 10 years = Present age of son + 10

= + 10 = years

So, Ratio = Age of the father after 10 yearsAge of son after 10 years = 52242452 =

Ratio =

(d) Age of father to the age of son when father was 30 years old.

When father was 42 years old then son age was 14: Age gap = 42 - 14 =

When father was 30 years old then son age = - =

So, Ratio = Age of fatherAge of son = 302230 =

Ratio =