If 45% of a number exceeds 20% of it by 96, then the number is:

Concept

When p% of a number N exceeds q% of the same number, the excess is (p − q)% of N.

Therefore, if the excess amount is known, form the equation ((p − q)/100) × N = excess and solve for N.

Application

1. Let the required number be N.

2. The difference between 45% and 20% is 25%, so the given excess is 25% of N.

3. Thus, (25/100) × N = 96.

4. Solving gives N = 96 × 100/25 = 384.

Cross-check

For N = 384, 45% of N is 172.8 and 20% of N is 76.8; their difference is 172.8 − 76.8 = 96, exactly as stated.

Hence, the required number is 384.