Exercise 7B
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
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
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 $\frac{1}{18}$
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
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
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
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
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
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
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
Q no 4 b and c
ReplyDeleteBoth are wrong
Values are interchanged
Thanks user for pointing out the mistake. We fixed it for you. ;)
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