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Which of these sets of numbers are in continued proportion? (i) 0.4, 3.6, 3.24 (ii) 7, 21, 63 (iii) 2.4, 9.6, 38.4
Question

Which of these sets of numbers are in continued proportion?
(i) 0.4, 3.6, 3.24
(ii) 7, 21, 63
(iii) 2.4, 9.6, 38.4

A.

(ii) and (iii)

B.

(i) and (ii)

C.

(i), (ii) and (iii)

D.

(ii) only

Correct option is A

Concept Used:
For three numbers a, b, and c to be in continued proportion, the ratio ab\frac{a}{b} must be equal to the ratio bc\frac{b}{c}​.
Solution:
(i) Checking for 0.4, 3.6, 3.24:

0.43.6=436=19\frac{0.4}{3.6} = \frac{4}{36} = \frac{1}{9}​​

3.63.24=360324=109\frac{3.6}{3.24} = \frac{360}{324} = \frac{10}{9}​​

Since abbc\frac{a}{b} \neq \frac{b}{c}​ these numbers are not in continued proportion.
(ii) Checking for 7, 21, 63:

721=13.\frac{7}{21} = \frac{1}{3}.​​

2163=13\frac{21}{63} = \frac{1}{3}​​

Since ab=bc\frac{a}{b} = \frac{b}{c}​, these numbers are in continued proportion.
(iii) Checking for 2.4, 9.6, 38.4:

2.49.6=14\frac{2.4}{9.6} = \frac{1}{4}​​

9.638.4=14\frac{9.6}{38.4} = \frac{1}{4}​​

Since ab=bc\frac{a}{b} = \frac{b}{c}​​, these numbers are in continued proportion.
Thus, statement(ii) and (iii) are correct.

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