Question

The sum of the numerator and denominator of a fraction is 12. If 1 is added to both the numerator and denominator the fraction becomes 1/3. Find the fraction.

Answer 1

let, the numerator be x

the denominator be y

the fraction : x/y

case - l:

x + y = 12 -------------------- (l) ×1

case - ll:

x + 1/y + 1 = 1/3

3x +3 = y + 1

3x - y = - 2 -----------------------(ll) ×1

3x - y = - 2

x + y = 12

___________

2x = 10

x = 5 -------------------- (lll)

putting (lll) in (l),

5 + y = 12

y = 12 - 5

y = 7

therefore, the fraction : 5/7

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