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