Quantitative Aptitude - MCQ Practice Questions

# Work Rate Problem Solution

[To solve tank filling problems, we must find each pipe's work rate (fraction of tank filled per hour), then track cumulative work.]

Step 1: Find Individual Work Rates

[Pipe A completes the tank in 20 hours, so its hourly rate is $\frac{1}{20}$ of the tank. Pipe B completes it in 30 hours, so its rate is $\frac{1}{30}$ of the tank.]

Step 2: Calculate Work Done in First 6 Hours (Both Pipes Working)

[When both pipes work together for 6 hours, we add their rates and multiply by time:]

Step 3: Find Remaining Work

[Half the tank is already filled, so the remaining work is:]

Step 4: Calculate Time for Pipe A Alone to Finish

[Only Pipe A continues at rate $\frac{1}{20}$ tank/hour. Using Time = Work ÷ Rate:]

Pipe A needs 10 hours to finish filling the tank.

Pipe A fills the tank in 20 hours.

So, work done by A in 1 hour:

20

1

​

Pipe B fills the tank in 30 hours.

So, work done by B in 1 hour:

30

1

​

Together, in 1 hour they fill:

20

1

​

+

30

1

​

LCM of 20 and 30 is 60:

=

60

3+2

​

=

60

5

​

=

12

1

​

So together they fill

12

1

​

of the tank per hour.

In 6 hours, they fill:

6×

12

1

​

=

12

6

​

=

2

1

​

So, half the tank remains.

Now only Pipe A works.

Pipe A fills

20

1

​

of the tank per hour.

Time to fill remaining

2

1

​

tank:

20

1

​

2

1

​

​

=

2

1

​

×20=10

Therefore, Pipe A will take:

10 hours

​

to finish filling the tank.

Answer: (D) 10 hours