The sum of the numerator and denominator of a fraction is 11. If 1 is added to…

Let the fraction be x/y, where x is the numerator and y is the denominator.

Given: x + y = 11 ... (1)

On adding 1 to the numerator and subtracting 2 from the denominator, the fraction becomes 2⅓ = 7/3.

So, (x + 1)/(y − 2) = 7/3 ... (2)

Cross-multiplying (2): 3(x + 1) = 7(y − 2) → 3x + 3 = 7y − 14 → 3x − 7y = −17 ... (3)

From (1): x = 11 − y. Substitute into (3): 3(11 − y) − 7y = −17 → 33 − 3y − 7y = −17 → 33 − 10y = −17.

So, 10y = 50 → y = 5, and x = 11 − 5 = 6.

Therefore, the fraction is 6/5.

Verification: 6 + 5 = 11, and (6 + 1)/(5 − 2) = 7/3 = 2⅓. Both conditions are satisfied.