Question

P and Q are working on an assignment. P takes 3 hours to type 20 pages on a computer. While Q takes 4 hours to type 25 pages. How much time will they together take to type an assignment of 620 pages working on two different computers?

• A. 64 hrs
• B. 48 hrs
• C. 40 hrs
• D. 60 hrs

Hint:

In work problems with typing or production, always convert data into rate per hour (or per unit time). Then add rates for combined work and divide total task by combined rate.

Answer 1

The Correct Option is B

Step 1: Rate of work of P 
P types 20 pages in 3 hours. 
So, P's typing rate = \( \frac{20}{3} \) pages per hour. 
Step 2: Rate of work of Q 
Q types 25 pages in 4 hours. 
So, Q's typing rate = \( \frac{25}{4} \) pages per hour. 
Step 3: Combined rate of P and Q 
\[ \text{P's rate} + \text{Q's rate} = \frac{20}{3} + \frac{25}{4} \] 
Take LCM of 3 and 4 = 12: 
\[ \frac{80}{12} + \frac{75}{12} = \frac{155}{12} \] 
So, together they type \( \frac{155}{12} \) pages per hour. 
Step 4: Time required for 620 pages 
\[ \text{Time} = \frac{\text{Total pages}}{\text{Combined rate}} = \frac{620}{\tfrac{155}{12}} = 620 \times \frac{12}{155} \] 
Simplify: \( 620 \div 155 = 4 \). 
\[ = 4 \times 12 = 48 \, \text{hours} \] 
\[ \boxed{48 \, \text{hours}} \]

Answer 2

Treating this like two pipes filling the same job (typing 620 pages) gives another route to the answer, and each option can be checked against the combined typing rate.

1. 64 hrs: The combined rate of P and Q is \(\dfrac{20}{3}+\dfrac{25}{4}=\dfrac{155}{12}\) pages per hour. In 64 hours they would type \(64\times\dfrac{155}{12}\approx826.7\) pages, far more than the 620 pages required, so 64 hours is too long.
2. 48 hrs: In 48 hours, they type \(48\times\dfrac{155}{12}=4\times155=620\) pages exactly, matching the assignment size.
3. 40 hrs: In 40 hours they would type \(40\times\dfrac{155}{12}\approx516.7\) pages, which falls short of 620, so this is too little time.
4. 60 hrs: In 60 hours they would type \(60\times\dfrac{155}{12}=775\) pages, well beyond the 620 needed, so this overshoots.

An independent check confirms the same figure: if P alone would take \(620\div\frac{20}{3}=93\) hours and Q alone would take \(620\div\frac{25}{4}=99.2\) hours to type the 620 pages, then working together like two pipes, \(\dfrac{1}{T}=\dfrac{1}{93}+\dfrac{1}{99.2}=\dfrac{16}{1488}+\dfrac{15}{1488}=\dfrac{31}{1488}=\dfrac{1}{48}\), so \(T=48\) hours.

So the correct answer is 48 hrs.