Question

17. The sum of the numerator and denominator of a fraction is 12. If 1 is
added to both the numerator and the denominator, the fraction becomes
3/4. Find the fraction.​

Answer 1

Given :-

• The sum of the numerator and denominator of a fraction is 12. If 1 is added to both the numerator and the denominator, the fraction becomes 3/4.

To find :-

• Required fraction

Solution :-

Let the numerator be x then denominator be y

Sum of the numerator and denominator of a fraction is 12.

• x + y = 12 ----(i)

If 1 is added to both the numerator and the denominator, the fraction becomes 3/4.

• x + 1/y + 1 = 3/4

→ 4(x + 1) = 3(y + 1)

→ 4x + 4 = 3y + 3

→ 4x - 3y = 3 - 4

→ 4x - 3y = - 1 ------(ii)

Multiply (i) by 3 and (ii) by 1

• 3x + 3y = 36
• 4x - 3y = - 1

Add both the equations

→ 3x + 3y + 4x - 3y = 36 - 1

→ 7x = 35

→ x = 35/7

→ x = 5

Put the value of x in equation (i)

→ x + y = 12

→ 5 + y = 12

→ y = 12 - 5

→ y = 7

Hence,

• Required fraction

• Numerator/denominator

• x/y = 5/7