# The Sum of the Numerator and Denominator of a Fraction is 11. If 1 is Added to the Numerator and 2 is Subtracted from the Denominator, It Becomes 2/3. The Fraction is?

### Computer MCQs Series for PPSC, FPSC – Most Repeated MCQs | Set 6

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## Explanation

• The sum of the numerator and denominator of a fraction is 11.
• If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes 2/3. The fraction can be figure out in this way.

Let suppose y shows numerator and z shows denominator in a fraction.

The sum of numerator and denominator is 11.

y + z = 11 ________ (i)

When 1 is added in y and 2 is taken away from z then

(y + 1)/(z – 2) = 2/3 ________ (ii)

By solving both equations simultaneously, we can easily find out the fraction (y/z = 3/8).

Fraction = ?

## Solution

Let suppose

Let suppose y shows numerator and z shows denominator in a fraction.

According to first given condition

y + z = 11 ________ (i)

Multiplying both sides of equation (i) with 2

2y + 2z = 22 ________ (A)

According to second given condition

(y + 1)/(z – 2) = 2/3 ________ (ii)

3(y + 1) = 2(z – 2)

3y + 3 = 2z – 4

3y – 2z = -7 ________ (B)

2y + 3y + 2z – 2z = 22 – 7

5y = 15

y = 15/5

y = 3

Put y = 3 in equation (i)

3 + z = 11

z = 11 – 3

z = 8

## Conclusion

The sum of the numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes 2/3. The fraction is 3/8.