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

  Exercise 8 B

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

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Question 1 

Determine whether the following number are in proportion or not: 

(i) $\frac{1}{2}, \frac{1}{4}, \frac{1}{7}, \frac{1}{14}$

Sol: Product of Extreme =$\frac{1}{2} \times \frac{1}{14}=\frac{1}{28}$

Product of means = $\frac{1}{4} \times \frac{1}{7}=\frac{1}{28}$

∵ Product  of  Extreme= Product of means 

$\frac{1}{28}=\frac{1}{28}$

$\therefore \frac{1}{2},\frac{1}{4},\frac{1}{7},\frac{1}{14}$ are proportion 

$\therefore \quad 12,15,4,5$ are in proportion 

(ii) $12,15,4,5$

Sol: $12 \times 5=60$

$15 \times 4=60$

60=60

(iii) $2,3 \frac{1}{2}, 3,4 \frac{1}{2}$ = $2, \frac{7}{2}, 3, \frac{9}{2}$

Sol: $2 \times \frac{9}{2}=9$ ; $\frac{7}{2} \times 3=\frac{21}{2}$

∵ Product of extreme≠ Product of means 

$2,3 \frac{1}{2}, 3,4 \frac{1}{2}$ are not in proportions

(iv) $1.2,1.6,0.9,1.2$

Sol: $1.2 \times 1.2=1.44$ ; $1.6 \times 0.9=1.44$

∵ Product of extreme = product of means 

1.44= 1.44 

∵ $1.2,1.6,0.9,1.2$ are in Proportion 

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Q2 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper

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Question 2

Find the value of x in each of the given proportions: 

(i) 0.9: 0.6:: x : 3 

Sol: $0.6 \times x=0.9 \times 3$

$x=\frac{0.9 \times 3}{0.6}=4.5$

(ii)  $x: 5:: 28: 35$

Sol: $x \times 35=5 \times 28$ 

=x = $\frac{5 \times 28}{35}$

= x=4

(iii) $1.6: x:: 0.12: 0.24$ 

Sol:  $x \times 0.12=1.6 \times 0.24$

$\Rightarrow \quad x=\frac{1.6 \times 0.24}{0.12}$

=x = 3.2 

(iv) $\frac{1}{15}: \frac{1}{4}:: x: \frac{1}{5}$

 

Sol: $\frac{1}{4} \times x=\frac{1}{15} \times \frac{1}{5}$

$\Rightarrow x=\frac{4}{75}$

(v) $16: x:  x: 25$

Sol: $\Rightarrow x \times x=16 \times 25$

$\Rightarrow x^{2}=16 \times 25$

$\Rightarrow x=4 \times 5$

$\Rightarrow x=20$

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Q3 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper

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Question 3

Find the fourth proportional to : 

(i) $8, 32,17, x$

Sol: $8 \times x=32 \times 17$

$x=\frac{32 \times 17}{8}$

x = 68

(ii) $8.1,1.2,2.7,x$ 

Sol: 

$8.1 \times x=1.2 \times 2.7$

x = $\frac{1.2 \times 2.7}{8.1}$

x= 0.4

(iii) $\frac{1}{3}, \frac{1}{5}, \frac{1}{7}, x$

Sol: $\frac{1}{3} \times x=\frac{1}{5} \times \frac{1}{7}$

$x=\frac{3}{35}$ Ans

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Question 4

Find the mean proportional between 

(i) 144 and 225

Sol: Let x be the mean proportional between 144 and 225

Then $x^{2}=144 \times 225$

$x=\sqrt{144 \times 225}$

$x=12 \times 15$

$x=180$

(ii) 0.32 and 0.08 

Sol: Let x be the mean proportional between 0.32 and 0.08 

Then , $x^{2}=0.32 \times 0.08$

$x^{2}=0.0256$

$x^{2}=\frac{256}{10000} \Rightarrow x=\sqrt{\frac{256}{10000}}$

$x=\frac{16}{100}$

$\Rightarrow \quad x=0.16$

(iii) $\frac{1}{36}$ and $\frac{1}{9}$

Let $x$, Then $x^{2}=\frac{1}{36} \times \frac{1}{9}$

$x=\sqrt{\frac{1}{36} \times \frac{1}{9}}$

$x=\frac{1}{6} \times \frac{1}{3}$

$x=\frac{1}{18}$

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Q5 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper

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Question 5

Find the third proportional to: 

(i) 32; 16 

Sol: Let the third proportional to 32 and 16 be x 

= 32, 16 , 16 ,x 

= $32 \times x=16 \times 16 \Rightarrow x=\frac{16 \times 16}{32}$

=x =8 Answer

(ii)  $4 \frac{1}{6}, 5$

Sol: $\frac{25}{6}, 5,5,x$

= $\frac{25}{6} \times 4=5 \times 5$

$\Rightarrow \quad x=25 \times \frac{6}{25}$

= x =6 answer 

(iii) 4.2 , 0.7 

Sol: 4.2 , 0.7 , 0.7 ,x 

$4.2 \times x=0.7 \times 0.7$

x =$\frac{7}{60}$

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Question 6

Show that 6, 36 , 216 are in continued proportion

Sol : 

6, 36, x ,216 

= $36 \times 21=6 \times 216$

$x=\frac{6 \times 216}{36}$

x= 36

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Question 7

If 25 persons can dig a trench 36 m long in one day . Then find the number of persons required to dig a trench 108m long in one day. 

Sol : 

$25: 36:: x: 108$

$36 \times x=108 \times 25$ 

x=  $\frac{108 \times 25}{36}$

x= 75

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Question 8

The label on a flavoured milk bottle states that there is 1.5 g of fat in 200ml. If you drink 500ml of that milk , how much fat would you be getting ? 

Sol : 

$1.5: 200:: x: 500$

= $200 \times x=1.5 \times 500$

x=$\frac{1.5 \times 500}{200}$

=3.75g 

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Question 9

Rajat can type 3200 words in one hour . How many wards can be type in 15 minutes? 

Sol : 

3200: 60:: x :15

=$60 \times x=3200 \times 15$

x =  $\frac{3200 \times 15}{60}$

x = 800 words