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Two numbers are in the ratio $\frac{1 \frac{1}{2}}{2 \frac{2}{3}}$ . But if each number is increased by $15$ , then the ratio becomes $\frac{1 \frac{2}{3}}{2 \frac{1}{2}}$ . What are the numbers?

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An Intiative by Sri Chaitanya

27, 42

36, 48

27, 48

27, 36

answer is C.

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Detailed Solution

Given, the ratio of two numbers is

\frac{1 \frac{1}{2}}{2 \frac{2}{3}}

.
⇒

\frac{\frac{3}{2}}{\frac{8}{3}} = \frac{9}{16}

Also, when each number is increased by

15

, then the ratio becomes

\frac{1 \frac{2}{3}}{2 \frac{1}{2}} = \frac{2}{3}

.
Let

9 x

and

16 x

be the two numbers.
According to the given condition,

\Rightarrow

\frac{9 x + 15}{16 x + 15} = \frac{2}{3}

\Rightarrow

3 \times (9 x + 15) = 2 \times (16 x + 15)

\Rightarrow

27 x + 45 = 32 x + 30

\Rightarrow

5 x = 15

\Rightarrow x = 3

⇒

9 x = 9 \times 3

= 27

⇒

16 x = 16 \times 3

= 48

Therefore, the numbers are

27

and

48

.
Hence, the correct option is 3.

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