**Q) **Two pipes together can fill a tank in hours. The pipe with larger diameter takes 2 hours less than the pipe with smaller diameter to fill the tank separately. Find the time in which each pipe can fill the tank separately.

**Ans:**

Let’s consider the larger pipe takes X hours to fill the tank separately

hence, smaller pipe will take pipe X + 2 hours

Therefore, time taken together to fill the tank:

(given)

15 [(X + 2) + X ] = 8 X (X + 2)

30 X +30 = 8X^{2} + 16X

4X^{2 }– 7 X – 15 = 0

4X^{2 }– 12 X + 5 X – 15 = 0

(X – 3) (4X + 5) = 0

Since x , therefore X = 3

and X + 2 = 5

**Therefore, the pipe with larger diameter will take 3 hrs and smaller diameter pipe will take 5 hrs to fill the tank separately.**