Q) Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.

(Q 34 B – 30/2/2 – CBSE 2026 Question Paper)

Ans: 

Step 1: Let’s consider Volume of the tank is V

and larger diameter pipe fills the tank in X hrs

∴ The volume filled by larger diameter pipe in 1 hr =

∴ The volume filled by larger diameter pipe in 4 hr =

Step 2: Given that smaller diameter pipe takes 10 hours more than larger pipe to fill the pool

∴ Smaller diameter pipe fills the tank in (X + 10) hrs

∴ The volume filled by smaller diameter pipe in 1 hr =

∴ The volume filled by smaller diameter pipe in 9 hrs =

Step 3: Given that volume filled by larger diameter pipe in 4 hr + volume filled by smaller diameter pipe in 9 hrs = Half Volume of the tank

∴ 

∴  (∵ V is common factor on both sides)

∴ 

∴ 

∴  2 (13 X + 40} = X (X + 10)

∴  26 X + 80 = X ² + 10 X

∴ X ² + 10 X – 26 X – 80 = 0

∴ X ² – 16 X – 80 = 0

∴ X ² – 20 X + 4 X – 80 = 0

∴ X(X – 20) + 4 (X – 20) = 0

∴ (X – 20) (X + 4)= 0

∴ X = 20 hrs and X = – 4 hrs

Step 4: Here, we reject X = -4 because value of time taken can not be negative.

∴ X = 20 hrs

∴ Time by smaller diameter pipe = 20 + 10 = 30 hrs

Therefore, time taken by larger pipe is 20 hrs and time taken by smaller pipe is 30 hrs.

Check:
∵ Larger pipe fills in 20 hrs
∴ tank filled in 4 hrs = 4 V/20 = V/5
∵ Smaller pipe fills in 30 hrs
∴ tank filled in 9 hrs = 9 V/30 = 3V/10
∴ tank filled together = V/5 + 3V/10 = 5V/10 = V/2
Since it meets the given condition, hence our answer is correct.

Please press the “Heart”, if you liked the solution.