Question

A typing work is done by two persons A and B. A and B together can type a booklet in 4 hours, but A alone takes 12 hours to type the booklet. How many hours required for B to type the booklet?

• A. 3 hours
• B. 4 hours
• C. 5 hours
• D. 6 hours

Hint:

For combined work, subtract individual rates to find the unknown worker’s efficiency.

Answer 1

The Correct Option is D

To find out how many hours B requires to type the booklet alone, we must understand the work completion rates of A and B.

1. First, determine the combined work rate of A and B working together. If they can complete the booklet in 4 hours together, their combined work rate is \(\frac{1}{4}\) of the booklet per hour.
2. Next, find A's individual work rate. A takes 12 hours alone, so A's work rate is \(\frac{1}{12}\) of the booklet per hour.
3. Using these work rates, we can find B's work rate by subtracting A's rate from their combined rate:

\(\text{Combined work rate} = \frac{1}{4}\)
\(\text{A's work rate} = \frac{1}{12}\)
\(\text{B's work rate} = \text{Combined work rate} - \text{A's work rate}\)
\(\Rightarrow \text{B's work rate} = \frac{1}{4} - \frac{1}{12}\)

1. Simplify the equation to find B's work rate:

\(\frac{1}{4} = \frac{3}{12}\)
\(\frac{1}{4} - \frac{1}{12} = \frac{3}{12} - \frac{1}{12} = \frac{2}{12} = \frac{1}{6}\)

1. Therefore, B's work rate is \(\frac{1}{6}\) of the booklet per hour, meaning B can complete the booklet in 6 hours.

Thus, B requires 6 hours to type the booklet alone.