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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 â€“ 2) = 2/3 ________ (ii)

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

## To Find

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 â€“ 2) = 2/3 ________ (ii)

3(y + 1) = 2(z â€“ 2)

3y + 3 = 2z â€“ 4

3y â€“ 2z = -7 ________ (B)

Adding equation (A) and (B)

2y + 3y + 2z â€“ 2z = 22 â€“ 7

5y = 15

y = 15/5

y = 3

Put y = 3 in equation (i)

3 + z = 11

z = 11 â€“ 3

z = 8

**Fraction = 3/8 answer**

## 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.