Quantitative Aptitude - MCQ Practice Questions

Let boys = 3x, girls = 2x. Total weight = (3x × 60) + (2x × 55) = 180x + 110x = 290x. Average = 290x / 5x = 58 kg.

# 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

To find the average work rate per day for the remaining workers, we must calculate each worker's individual rate, then find the combined rate after A leaves.

Step 1: Calculate individual work rates

Worker A completes the job in 12 days, so A's rate = $\frac{1}{12}$ job/day

Worker B completes the job in 15 days, so B's rate = $\frac{1}{15}$ job/day

Worker C completes the job in 20 days, so C's rate = $\frac{1}{20}$ job/day

Step 2: Find the combined rate of all three workers

Finding the LCM of 12, 15, and 20:

Step 3: Calculate work done in first 2 days

In 2 days, all three workers complete:

This information establishes context, but the question asks for the average rate of remaining workers (B and C) after A leaves.

Step 4: Find average work rate of remaining workers (B and C)

Number of remaining workers = 2

**Answer: The average work rate per day for the remaining workers is $\frac{7}{120}$ (Option A)**