Exercise R1 | Class 10 | Mathematics | Revision Exercise

1. Which of the following ratios are in proportion?
(a) $\ 12:21$ and $\ 32:56$
(b) $\ 18:30$ and $\ 14:21$
(c) $\ 22:33$ and $\ 33:24$
(d) $\ 24:28$ and $\ 20:25$
Ans. (a) $\ 12:21$ and $\ 32:56$
Explanation: we have the condition for two ratios to be in proportion as,
Product of the means = Product of the extremes.
Here, Product of the means = 21×32 = 672
Product of the extremes = 12×56 = 672
⸫ The condition is satified.


2. Which of the following sets of numbers are in proportion?
(a) 2, 6, 6, 8
(b) 10, 20, 30, 60
(c) $\ p, pq, p^2q, q^2$
(d) 6, 20, 4, 30
Ans. (b) 10, 20, 30, 60
Explanation: 20×30 = 10×60


3. Fill in the blanks:
(i) The area of the circle, $\ A = \pi r^2$
If $\ A$ increases then $\ r$ ____. If $\ r$ decreases then $\ A$ _____.
Ans. increses, decreases.

(ii) The relation between distance $\ (d)$ and time $\ (t)$ of a moving car is as given in the following table-

$\ t$	1	2	3	4	5	6	?	?	?
$\ d$	4	8	12	16	20	?	28	?	36

Fill in the blanks:
(a) $\ t$ and $\ d$ varies _____.
Ans. directly.
Explanation:
Since, $\ \frac{t}{d}=\frac{1}{4}= a~ constant$


(b) If $\ t$ = 6 then $\ d$ = ____
Ans. 24.
Explanation:
We have, $\ t=1$ and $\ d=4$ for all the cases,
Since, $\ t$ is directly proportional to $\ d$

⸫ $\ t:d=t:d ⇒ t:d=1:4$

$\ ⇒ \frac{6}{d}=\frac{1}{4} ⇒ 4×6=d ⇒ d =24$

(c) If $\ d$ = 28 then $\ t$ = ____
Ans. 7.
Explanation:
We have, $\ t=1$ and $\ d=4$ for all the cases,
Since, $\ t$ is directly proportional to $\ d$

⸫ $\ t:d=t:d ⇒ t:d=1:4$

$\ ⇒ \frac{t}{28}=\frac{1}{4} ⇒ t = \frac{28}{4} ⇒ t = 7$

(d) If $\ d$ = 36 then $\ t$ = ____
Ans. 9.
Explanation:
We have, $\ t=1$ and $\ d=4$ for all the cases,
Since, $\ t$ is directly proportional to $\ d$

⸫ $\ t:d=t:d ⇒ t:d=1:4$

$\ ⇒ \frac{t}{36}=\frac{1}{4} ⇒ t = \frac{36}{4} ⇒ t = 9$


4. If $\ p\propto q$ and when $\ p=6$ then $\ q=30$. Now if $\ p=2$ then what is the value of $\ q$?
(i) 12
(ii) 20
(iii) 10
(iv) 15
Ans. (iii) 10.
Explanation:
Since, $\ p$ is directly proportional to $\ q$

⸫ $\ p:q=p:q ⇒ 6:30=2:q$

$\ ⇒ \frac{6}{30}=\frac{2}{q} ⇒ q = \frac{30×2}{6} ⇒ q = 10$


5.The value of $\ y$ in the blank space of the following table is

$\ x$	1	2	4	8
$\ y$	32	16	8	-

(i) 8
(ii) 6
(iii) 4
(iv) 2
Ans. 4.
Explanation:
Let $\ y_4 (=y)$ be the corresponding value of 8 which is to be found out.
Since, $\ x$ is inversely proportional to $\ y$.
⸫ $\ x_1:x_4=y_4:y_1 ⇒ 1:8=y_4:32$
$\ ⇒ \frac{1}{8}=\frac{y_4}{32} ⇒ y_4 = \frac{32}{8} ⇒ y_4 = 4$

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