Question

The denominator of a rational number is greater than its numerator by 7. If the number is increased by 1 and the denominator is decreased by 2, the number obtained is 3/5. Find the rational number.​

Answer 1

Explanation:

Let x be the fraction's numerator.

Then (x + 7) is the fraction's denominator.

Numerator increased by 1 => (x + 1)

Denominator decreased by 2 => (x + 5)

We have (x + 1) / (x + 5) = 3/5.

Therefore by cross-multiplication,

3(x + 5) = 5(x + 1).

=> 3x + 15 = 5x + 5

=> 2x = 10

=> x = 5.

Hence the original fraction is 5/12.