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Given a fraction, whose numerator when multiplied by 2 is 2 more than the denominator. After adding 3 to the numerator and to the denominator, the new fraction is $23$ . Find the fraction.

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712

45

325

225

answer is A.

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Detailed Solution

Given a fraction in which, numerator when multiplied by 2 is 2 more than the denominator.
After adding 3 to the numerator and to the denominator, the new fraction is

23

.
Let the numerator of fraction be

' p'

.
According to the question,
Denominator

= 2 p − 2

.
The fraction is

p 2 p − 2

-(i)
After adding ‘3’ to numerator and denominator,
The new fraction is

p + 3 2 p + 1

.
From given,

⇒ p + 3 2 p + 1 = 23

Cross-multiplying both side:

⇒

3 (p + 3) = 2 (2 p + 1)

⇒ 3 (p) + 3 (3) = 2 (2 p) + 2 (1) ⇒ 3 p + 9 = 4 p + 2 ⇒ 4 p − 3 p = 9 − 2 ⇒ p = 7

Substituting value of

' p'

in (i):

⇒ 7 2 (7) − 2 ⇒ 7 14 − 2 ⇒ 712

The fraction is

712

.
Hence, option 1 is correct.

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