SChand Composite Mathematics Class 7 Chapter 8 Ratio , Proportion , Unitary Method Exercise 8A

Exercise 8 A 

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Q1 | Ex-8A | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper

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Question 1

Express each of the following ratios in the simplest form: 

(i) $28: 63$ 

Sol: $\frac{28}{63}$

= 4: 9

(ii) 105: 133 

Sol: $\frac{105}{133}$ 

= 15: 19

(iii) 0.4: 0.6 66

Sol: $\frac{0 \cdot 4}{0 \cdot 6}$ 

= 2: 366

(iv) $2.7: 9$ 

Sol: $\frac{27}{90}$ 

=3:10

(v) $\frac{1}{4}: \frac{1}{9}$ 

Sol: $\frac{1}{4} \div \frac{1}{9}$

= $\frac{1}{4} \times \frac{9}{1} \quad \Rightarrow 9: 4$

(vi) $3 \frac{1}{2}: 2 \frac{1}{4}$

Sol: $\frac{7}{2} \div \frac{9}{4}$ 

= $\frac{7}{2} \times \frac{4}{9}$ 

= 14: 9

(vii) $\frac{1}{4}: \frac{1}{8}: \frac{1}{10}$

Sol: L.C.M of 4, 8 , 10 is = 40

$\frac{1}{4} \times 40: \frac{1}{8} \times 40: \frac{1}{10} \times 40=10: 5: 4$

(viii)  $1 \frac{3}{4}: 2 \frac{2}{3}: 1 \frac{5}{6}$ 

Sol: $\frac{7}{4}: \frac{8}{3}: \frac{11}{6}$

(xi)  $125 \mathrm{~g}: 1 \mathrm{~kg}$ 

Sol: $\frac{125}{1000}$

=1: 8

(x) 4 days : 2 weeks 

4 days: 14 days 

Sol: $\frac{4}{14}$ 

= 2: 7

(xi) 36 minutes to $1 \frac{1}{2}$ Hours

Sol: 36 mint to 90 Min

(xii) 76 ml

Sol:  1L 710ML 

= 76 ml : 1710ML 

 $\Rightarrow \frac{76}{1710}$ 

= 2: 45

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Question 2

There are 2500 students in a school out of them 1100 are girls and the rest are boys , find the ratio of: 

Sol: No of girls= 1100

No of boys = 2500- 1100= 1400

(i) Number of boys to number of girls 

1400 : 1100 = 14: 11

(ii) Number of girls to number of students 

1100: 2500 = 11: 25 

(iii) Number of students to number of boys 

2500: 1400= 25:14

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Question 3

The given figure shows a small garden. The shaded area is reserved for planting flowers and the rest of the area is for grass. Find the ratio of the area of the garden reserved for planting flowers to the area reserved for grass.

Sol: Area for flowers =  $8 \times 3=24 \mathrm{~m}^{2}$

Area for grass = Total area - area of flowers 

$\Rightarrow 12 \times 5-24$

$\Rightarrow \quad 60-24=36 \mathrm{~m}^{2}$

Area of flower : Area of for grass

$24: 36 \Rightarrow \frac{24}{36}=2: 3$

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Question 4

If the ratio of the length to the breadth of  a rectangle be 5: 3 and its perimeter is 144m, find the length of the rectangle . 

Sol: Let the length = 5x & Breadth = 3x 

Perimeter of rectangle = $2 \times(l+b)$

$2 \times(5 x+3 x)=144$

$2 \times 8 x=144 \Rightarrow x=\frac{144}{16}=x=9$

Length= 5x = $5 \times 9=45 \mathrm{~m}$ Ans

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Question 5

Divide Rs 7400 among three people A, B , C in the ratio 3 : 5: 12 

Sol:     Let the amount = 3x : 5x : 12x 

3x+5x+12x=7400

20x =7400

x $=\frac{7400}{20}$

x=370

A' s Amount =$3 \times 370=1100$

B's Amount =$5 \times 370=1850$

C's Amount = $12 \times 370=4440$

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Question 6

Divide 104 pencils among three children in the Ratio $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$

Sol : 

L.C.M of 2,3,4 = 12 

Simplified Ratio= $12 \times \frac{1}{2}: 12 \times \frac{1}{3}: 12 \times \frac{1}{4}$

$=6: 4: 3$

Let Sum = $6 x+4 x+3 x=104$

$\Rightarrow \quad 13 x=104$

$\Rightarrow \quad x=\frac{104}{13}$

x= 8

1st share = $6 \times 8=48$ pencils

2nd share = $4 \times 8=32$ pencils

3rd share = $3 \times 8=24$ pencils.

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Question 7

The angles of a quadrilateral are in the ratio 1: 2: 3 : 4 . If the sum of the angles of 9 quadrilateral is 360'. Find the measure of each angle. 

Sol: Let angles = 1x : 2x : 3x : 4x 

1x + 2x+3x + 4x = $360^{\circ} \Rightarrow 10 x=360^{\circ}$

x = $36^{\circ}$ 

First angle = $1 \times 36=36^{\circ}$

Second angle  = $2 \times 36=72^{\circ}$

3rd angle = $3 \times 36=108^{\circ}$

4th angle = $4 \times 36=144^{\circ}$ 

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Question 8

If a: b = 5: 7 and b: c = 14: 15, find a: c 

Sol: $\frac{a}{b}=\frac{5}{7} \quad ; \frac{b}{c}=\frac{14}{15}$

$\frac{a}{b} \times \frac{b}{c}=\frac{5}{7} \times \frac{14}{15}$

= $a: c=2: 3$

(ii) If x: y = 2: 7 and y: z = 9: 11 find x: y : z 

Sol: $\frac{x}{y}=\frac{2}{7}$ , $\frac{y}{z}=\frac{9}{11}$

L.C.M = 7,9 is 64 : To find x: y: z we have to make y equal 

$\frac{x}{y}=\frac{2 \times 9}{7 \times 9}=\frac{18}{63} ; \quad \frac{y}{2}=\frac{9}{11 \times 7} \times \frac{7}{7}=\frac{63}{77}$

$x: y=18: 63 ; \quad y: z=63: 77$

$x: y: z=18: 63: 77$

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Question 9

If l: m= $1 \frac{1}{2}: 1 \frac{3}{4}$ and m: n $2 \frac{1}{3}: 4 \frac{1}{5}$

Sol: 

l: m =$\frac{3}{2}: \frac{7}{4}$= $\frac{3}{2} \div \frac{7}{4}$

=$\frac{3}{2} \times \frac{4}{7}$

$\frac{6}{7}=\frac{l}{m}$

m: n =$\frac{7}{3}: \frac{21}{5}$

$\frac{7}{3} \div \frac{21}{5}=$ $\frac{7}{3} \times \frac{5}{21}$

= $\frac{5}{9}=\frac{m}{n}$

=$\frac{1}{m}=\frac{6}{7}$ 

=$\frac{m}{n}=\frac{5}{9}$

(i)  $\frac{l}{m} \times \frac{m}{n}$

 = $\frac{6}{7} \times \frac{5}{9}$

=10:21= l: n Answer

(ii) l: m: n 

Sol: 

$\frac{1}{m}=\frac{6}{7}$ 

$\frac{m}{n}=\frac{5}{9}$

$\frac{l}{n}=\frac{10}{21}$

$\frac{1}{m} \times \frac{m}{n} =\frac{l}{n}$

Taking L.C.M of 7 and 5 =35

$\frac{1}{m}=\frac{6}{7} \times \frac{5}{5}=\frac{30}{35}$ 

$\frac{m}{n}=\frac{5}{9} \times \frac{7}{7}=\frac{35}{63}$

$\frac{1}{m} \times \frac{m}{n} =\frac{l}{n}$

$\frac{30}{35} \times \frac{35}{63} =\frac{30}{63}$

 l : m : n = 30 : 35 : 63

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Question 10

Divide Rs 1545 between three people A, B and C such that A gets three fifths of what B gets and the ratio of the share of B to C is 6: 11

Sol : 

Let the common factor be x

∴B=6x , C=11x

$A=\frac{3}{5} of B$

$A=\frac{3}{5} \times 6x$

$A=\frac{18x}{5}$

A+B+C=1545

$\frac{18x}{5}+\frac{6x}{1}+\frac{11x}{1}=1545$

$18x \times 1+6x \times 5 + 11x \times 5=1545 \times 5$

$18x+30x+55x=1545  \times 5$

103x=1545×5

$x=\frac{1545 \times 5}{103}$

x=75

B' share = $6 \times 75=450$

C' share = $11 \times 75=825$

A' share = $\frac{18}{5} \times x=\frac{18}{5} \times 75=270$

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Question 11

The ratio of the expenditure to the saving of a family is 7 : 3. Find income if the expenditure is Rs 6300.

Sol: Let Exp. saving= 7x: 3x 

Income = Exp. + saving 

$=7 x+3 x=10 x$

Given exp = 6300

7x = 6300 = $x=\frac{6300}{7} \Rightarrow 21=900$

Income = 10x =  $10 \times 900=9000$ Answer 

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Question 12

The ratio between the present age of p and Q is 3: 4 respectively . If Q'S Present age is 20 

Year what will be the ratio of the ages after 5 years? 

Sol: Let ratio of P and Q = 3x: 4x

Q's present age 4x = $20 \Rightarrow 21=\frac{20}{4}=5$

P 's Present age = $3x=3 \times 5=15$

After  5 years p's age = $15+5=20$ yr 

Q's age = 20+5 = 25 yr 

Ratio P: Q = 20 : 25= 4: 5 answer 

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Question 13

Rina lost her weight in the ratio 5: 3 . Her original weight was 80 kg . what is her new weight ? 

Sol: Original weight = $5 x=80 \Rightarrow x=\frac{80}{5}$

x= 16

New weight = 3x = $3 \times 16=48$kg