Rahul and Shyam, working together, can do a piece of work in 5 hours; Rahul alone can do the same work in 15 hours. How much time will Shyam alone take to do that work?

Let's assume the total work is 15 units.

Rahul and Shyam, working together, can do a piece of work in 5 hours.

The efficiency of Rahul and Shyam working together = $$\frac{15}{5}$$ = 3 units/hour

Rahul alone can do the same work in 15 hours.

The efficiency of Rahul = $$\frac{15}{15}$$ = 1 unit/hour

The efficiency of Shyam = 3-1 = 2 unit/hour

Time taken by Shyam alone to do that work = $$\frac{15}{2}$$

= 7.5 hours