Question

# The denominator of a rational number is greater than its numerator by 3.If the numerator is increased by 8 and the denominator is decreased by 1, then new number becomes 53.The original number is:

A

B

C

D

Solution

## The correct option is B Let the numerator of rational number = x Denominator of a rational number = x + 3 When numerator is increased by 8, then new numerator = x + 8 When denominator is decreased by 1, then new denominator = x + 3 - 1 = x + 2 New number = 53 ⇒ x+8x+2 = 53 ⇒ 3x + 24 = 5x + 10 ⇒ 2x = 14  ⇒ x = 7 So, the original number will be 710

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