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 \emph{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: \( 620 \div 155 = 4 \).
\[ = 4 \times 12 = 48 \, \text{hours} \]
\[ \boxed{48 \, \text{hours}} \]