Question

There are two pipes, pipe M and pipe N to fill a tank. Pipe M alone can fill \({2}\over{3}\) of the empty tank's capacity in 24 hours. Pipe N alone can fill \({5}\over{6}\) of the empty tank's capacity in 60 hours. Both pipes fill water at their respective rates. How many hours will both pipes fill the empty tank together according to their capacity?

1. 30 hours
2. 36 hours
3. 24 hours
4. 32 hours

Answer 1

Correct Answer - Option 3 : 24 hours

Given:

Pipe M alone can fill \(\frac{2}{3}\) of the empty tank's capacity in 24 hours

Pipe N alone can fill \(\frac{5}{6}\) of the empty tank's capacity in in 60 hours

Formula Used:

Work = Efficiency × Time

Calculation:

Pipe M can fill 2/3 of empty tank in 24 hours 

⇒ Pipe M can fill the complete tank = (24 × 3)/2 hours

⇒ Pipe M can fill the complete tank = 36 hours 

Pipe N can fill 5/6 of empty tank in 60 hours

⇒ Pipe N can fill the complete tank = (60 × 6)/5 hours

⇒ Pipe N can fill the complete tank = 72 hours 

Total work = LCM of M's Time and N's Time 

LCM of 36 and 72 = 72 hours

Efficiency of M = 72/36 = 2 

Efficiency of N = 72/72 = 1 

Time taken by M & N together = 72/3 

⇒ 24 hours

∴ Both pipes will fill the empty tank together according to their capacity in 24 hours.