Question

Rajesh can check the quality of $1000$ items in $5$ hours and Rakesh can complete $75\%$ of the same job in $3$ hours. How much time is required for both of them to check $1300$ items, if Rakesh stops checking after $2$ hours?

Accepted Answer

C. Efficiency of Rajesh $= \frac{1000}{5} = 200	ext{ items/hr}$. Rakesh completes $75\%$ in $3	ext{ hrs} \implies$ Rakesh takes $\frac{100}{75} 	imes 3 = 4	ext{ hrs}$ to check $1000$ items. Efficiency of Rakesh $= \frac{1000}{4} = 250	ext{ items/hr}$. Let the total time taken by Rajesh be $t$ hours. Rakesh works for $2$ hours. $$	ext{Total Work} = 250 	imes 2 + 200 	imes t = 1300$$ $$500 + 200t = 1300 \implies 200t = 800 \implies t = 4	ext{ hours}$$.

Quality checking time

Explanation

Practise this under exam conditions