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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