Question

The denominator of a rational number is greater than its numerator by 5. If the numerator is
increased by 11 and the denominator is decreased by 14, the new number becomes 5. Find the
original rational number.

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Answer 1

Age of man: 37

Age of son 1: 8

Age of son 2: 3

Age of man at given condition: 37+x

Sum of age of sons at given condition: 8+x + 3+x

It is to be noted that the age of father is twice the sum of age of sons.

Therefore

37+x = 2( (8+x) + (3+x) )

37+x = 2( 11+2x )

37+x = 22+4x

3x = 15

x=5

Hence after 5 years your condition will satisfy.