Mohan takes 8 days less than the time taken by Ravi to finish a piece of work.…

Work-rate principle: if a person finishes a piece of work in n days, their work rate is 1/n of the work per day. When two people work together, their combined rate is the sum of their individual rates, and the time they take together is the reciprocal of that combined rate.

1. Let Ravi take x days to finish the work alone. Since Mohan takes 8 days less than Ravi, Mohan takes (x − 8) days.

2. Their individual work rates are 1/x and 1/(x − 8) work per day. Together they finish in 7.5 days, so the combined-rate equation is: 1/x + 1/(x − 8) = 1/7.5 = 2/15.

3. Multiply both sides by 15x(x − 8) to clear denominators: 15(x − 8) + 15x = 2x(x − 8).

4. Expand and simplify: 30x − 120 = 2x2 − 16x, which rearranges to 2x2 − 46x + 120 = 0, i.e. x2 − 23x + 60 = 0.

5. Solve this quadratic using the discriminant: √(232 − 4×60) = √(529 − 240) = √289 = 17, so x = (23 ± 17)/2, giving x = 20 or x = 3.

6. Reject x = 3, because Mohan's time (x − 8) would then be −5 days, which is impossible. So x = 20 days.

Cross-check: with x = 20, Ravi's rate is 1/20 and Mohan's rate is 1/12 (since 20 − 8 = 12). Their sum is 1/20 + 1/12 = 3/60 + 5/60 = 8/60 = 2/15, exactly the combined rate required to finish together in 7.5 days — confirming the value.

So Ravi alone takes 20 days to finish the work.