Exercise 8 B
Q1 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion ,
Unitary Method | myhelper
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
Q2 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper
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: $\Rightarrow x \times x=16 \times 25$
$\Rightarrow x^{2}=16 \times 25$
$\Rightarrow x=4 \times 5$
$\Rightarrow x=20$
Q3 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper
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
Q4 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper
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 $x^{2}=\frac{1}{36} \times \frac{1}{9}$
$x=\sqrt{\frac{1}{36} \times \frac{1}{9}}$
$x=\frac{1}{6} \times \frac{1}{3}$
$x=\frac{1}{18}$
Q5 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper
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 =$\frac{7}{60}$
Q6 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper
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
Q7 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper
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
Q8 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper
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
Q9 | Ex-8B | Class 7 | SChand Composite Maths | Ratio , Proportion , Unitary Method | myhelper
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
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