Tom and Jerry can paint a house together in 9 days. If Tom alone can paint the same house in 15 days, how long will it take for Jerry to paint the house alone?

Given: 

Time taken by Tom and Jerry together = 9 days

Time taken by Tom alone = 15 days

Concept Used: 

Total work = Efficiency $$\times$$ time

Solution: 

LCM of 15 and 9 = 45 

let the total work be 45 unit 

Efficiency of Tom + Jerry = $$\frac{45}{9} = 5 \, unit/day$$ 

Efficiency of Tom alone = $$\frac{45}{15} = 3 \, unit/day$$ 

Efficiency of Jerry = 5 - 3 = 2 unit/day 

Time taken by Jerry to complete work alone ;

 = $$\frac{45}{2}$$ 

Thus, time taken by Jerry is $$\bf \frac{45}{2} \, days$$​​