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Two numbers are in the ratio $7 : 11$ . If $7$ is added to each of the numbers, the ratio becomes $2 : 3$ . Then the numbers from the choices given below is-

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42, 66

49, 77

63, 99

77, 121

answer is B.

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Detailed Solution

It is given that, the ratio of numbers is

7 : 11

.
Let

7 x

and

11 x

be the required numbers.
The number

7

is added to

7 x, 11 x

numbers respectively to give the ratio

2 : 3

7 x + 7 11 x + 7 = 23

By cross multiplication, we get,

21 x + 21 = 22 x + 14

22 x − 21 x = 21 − 14

x = 7

Therefore, the numbers are given by,

7 x = 7 × 7 = 49

11 x = 11 × 7 = 77

Hence the numbers are

49, 77

.
Hence option 2) is correct.

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