Pipe A and B requires 80 minutes to fill the tank, pipe A and C requires 48/7 minutes to fill up the whole tank. If drain pipe is Pipe B and it requires 20 minutes to drain the whole tank then how much more efficient is pipe C when compared to pipe A?

Option 3 : 33.33%

Given:

Pipe A - Pipe B = 80 minutes

Pipe A + Pipe C = 48/7 minutes

Pipe B = 20 minutes (Drain pipe)

Formula:

If time taken by pipe A to fill tank is ‘a’ minutes and by pipe B is ‘b’ minutes to empty the tank then total time taken to fill the tank t ⇒ (1/t) = (1/ a) - (1/b)

If time taken by pipe A to fill tank is ‘a’ minutes and by pipe B is ‘b’ minutes then total time taken to fill the tank t ⇒ (1/t)= (1/a) + (1/b)

Calculation:

Let, time taken by pipe A = X minutes

⇒ 1/ 80 = (1/X) – (1/20)

⇒ 1/ 80 = 20 – X/(20X)

⇒ 20X = 1600 – 80X

⇒ X = 16 minutes

Hence, efficiency of A = (1/16) units

Let, time taken by pipe C = Y minutes

⇒ 7/ 48 = (1/16) + (1/Y)

⇒ 7/ 48 = Y + 16/16Y

⇒112 Y = 48Y + 768

⇒ 64 Y = 768

⇒ Y = 12 minutes

Hence, efficiency of C = (1/12) units

So, the C is more efficient than A by a percentage of:

= {/(1/16)} × 100 

⇒ Differrence in Efficiency = 33.33%

∴ Pipe C is 33.33% more efficient than pipe A.