S.chand publication New Learning Composite mathematics solution of class 7 Chapter 7 Ratio and Proportion and Unitary Method Exercise 7B

 Exercise 7B

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Q1 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 1

Find out whether the following groups of numbers are in proportion or not.

(a) 18, 20, 9, 10

Sol :

Product of extremes=18×10=180

Product of means=20×9=180

So, product of extremes=product of means

∴They are proportional

(b) 21, 6, 35, 10

Sol :

Product of extremes=21×10=210

Product of means=6×35=210

So, product of extremes=product of means

∴They are proportional

(c) 12, 18, 28, 12

Sol :

Product of extremes=12×12=144

Product of means=18×28=504

So, product of extremes≠product of means

∴They are not proportional

(d) 5.2, 3.9, 3, 4

Sol :

Product of extremes=5.2×4=20.8

Product of means=3.9×3=11.7

So, product of extremes≠product of means

∴They are not proportional

(e) 16, $3 \frac{1}{3}$, 18, $3\frac{3}{4}$

Sol :

Product of extremes$=16\times 3\frac{3}{4}=16\times \frac{15}{4}$

=60

Product of means$=3\frac{1}{3} \times 18=\frac{10}{3} \times 18$

=60

So, product of extremes=product of means

∴They are proportional

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Q2 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 2

Find x in the following proportions.

(a) x, 6, 55, 11

Sol :

$\frac{x}{6}=\frac{55}{11}$

11x=6×55

$x=\frac{6\times 55}{11}=30$

(b) 16, 18, x, 108

Sol :

$\frac{16}{18}=\frac{x}{108}$

$x=\frac{16 \times 108}{18}=96$

(c) 4, x, x, 16

Sol :

$x=\sqrt{4\times 16}$

x=8

(d) 7.5, 15, 5, x

Sol :

$\frac{7.5}{15} =\frac{5}{x}$

$x=\frac{15\times 5 \times 10}{75}$

∴x=10

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Q3 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 3

Find the fourth proportional to

(a) 32, 64, 6

Sol :

$\frac{32}{64}=\frac{6}{x}$

$x=\frac{6\times 64}{32}=12$

∴Fourth proportional is 12

(b) 8, 9, 24

Sol :

$\frac{8}{9}=\frac{24}{x}$

$x=\frac{9\times 24}{8}$

∴x=27

∴Fourth proportional is 27

(c) $\frac{1}{5}, \frac{1}{9}, \frac{1}{10}$

Sol :

$\frac{9}{5}=\frac{x}{10}$

$x=\frac{9\times 10}{5}=18$

∴Fourth proportional is $\frac{1}{18}$

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Q4 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 4

Find the mean proportional between

(a) 16 and 25

Sol :

$\frac{16}{x}=\frac{x}{25}$

$x^2=16\times 25$

$x=\sqrt{16 \times 25}$

∴x=4×5=20

∴Mean proportional is 20

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

Sol :

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

$x^2=\frac{9}{36}$

$x=\sqrt{\frac{1}{4}}$

∴$x=\frac{1}{2}$

∴Mean proportional is $\frac{1}{2}$

(c) 0.01 and 0.81

Sol :

$\frac{0.01}{x}=\frac{x}{0.81}$

$x^2=0.01\times 0.81$

$x=\sqrt{0.01 \times 0.81}$

∴x=0.09

∴Mean proportional is 0.09

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Q5 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 5

Find the third proportional to

(a) 25, 40

Sol :

25×x=40×40

$x=\frac{40\times 40}{25}=64$

∴x=64

∴Third proportional is 64

(b) 18, 30

Sol :

18×x=30×30

$x=\frac{30\times 30}{18}$

∴x=50

∴Third proportional is 50

(c) 3.9, 11.7

Sol :

3.9×x=11.7×11.7

$x=\frac{11.7\times 11.7}{3.9}$

∴x=35.1

∴Third proportional is 35.1

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Q6 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 6

Show that 5, 25, 125 are in continued proportions.

Sol :

Since 5×5=25

and 25×5=125

∴It can be said that they are in proportion

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Q7 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 7

If the cost of 8 m of cloth is Rs. 600, find the cost of 15 m of cloth.

Sol :

The cost of 8m of cloth is 600

The cost of 15m of cloth is $=\frac{600\times 15}{8}$

=1125

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Q8 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 8

When a man spends $\frac{5}{9}$ of his monthly income, he saves Rs. 3600 a month, find his income.

Sol :

Let , his monthly income be x

ATQ,

$x-\frac{5x}{9}=3600$

4x=3600×9

$x=\frac{3600 \times 9}{4}$

∴x=8100

His monthly income is 8100

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Q9 |  Ex-7B | SChand | New Learning Composite Maths | Class 7 |  Ratio and Proportion and Unitary Method | myhelper

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Question 9

After selling 85 copies of a book for every 100 copies printed, a publisher finds that 450 copies are left unsold. How many copies were printed?

Sol :

(100-85)=15 copies left

15 copies left for every 100 copies printed

450 copies left for every $\frac{100 \times 450}{15}= 3000$ or copies printed

Ans 3000 copies were printed

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Question 10

A truck requires 108 L of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?

Sol :

For covering 594 km distance diesel required 108L

For covering 1650 km distance diesel required $\frac{108\times 165}{594}$

=300 L

Ans 300L diesel will be required