Question 16

A can do a piece of work in 25 days and B in 20 days. They work together for 5 days and then A goes away. In how many days will B finish the remaining work ?

Solution

Let 100 units of work be there.

$$\eta_A=\ \ \frac{\ 100}{25}=4units\ per\ day$$

$$\eta_B=\ \ \frac{\ 100}{20}=5units\ per\ day$$

Amount of work done when they work together for 5 days = $$5\times\ \left(\eta_A+\eta_B\right)\ =\ 5\times\ \left(5+4\right)\ =\ 45\ units$$

Remaining work = 100-45 = 55 units

Time taken by B = $$\ \frac{\ 55}{5}=11\ days$$

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