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A fraction becomes $45$ when 1 is added to each of the numerator and denominator. However, if we subtract 5 from each of them, it becomes $1 / 2$ . Then, numerator of the fraction is

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answer is D.

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Detailed Solution

Given that, a fraction becomes

45

when 1 is added to each of the numerator and denominator and when subtract 5 from each of them, it becomes

12

.
Let the fraction be

x y

. Then, according to question,

x + 1 y + 1 = 45

⇒ 5 x + 5 = 4 y + 4 ⇒ 5 x − 4 y = − 1 … (i)

Also,

x − 5 y − 5 = 12 ⇒ 2 x − 10 = y − 5 ⇒ 2 x − y = 5 … (i i)

On multiplying Eq. (i) by 2 and Eq. (ii) by 5 and then subtracting Eq. (ii) from Eq. (i), we get,

10 x − 8 y = − 2 10 x − 5 y = 25

− 3 y = − 27

⇒ y = 9

Substituting the value of y in Eq. (i), we get,

5 x − 4 × 9 = − 1 ⇒ 5 x = − 1 + 36 ⇒ x = 7

Then fraction =

79

Therefore, the numerator of this fraction is 7.
Hence, option (4) is correct.

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