### Question 20

SSC-CGL 2020 Mar 3 Shift 2

A and B can complete a work in 20 and 25 days respectively. Both start together, but B leaves after 5 days. How many days will A take to complete the remaining work?

### Solution in Detail

Note: questions of this type we can take total work as any number, say, 1. In fact, it is possible to take total work as any variable such as W. But calculations can be simplified by taking total work as the LCM of the days taken by each worker to complete that work.Total work = LCM ($\displaystyle 20, 25$) = $\displaystyle 100$

1 day work of A = $\displaystyle \frac{100}{20} = 5$

1 day work of B = $\displaystyle \frac{100}{25} = 4$

1 day work of A+B = $\displaystyle 5 + 4 = 9$

A + B work for $\displaystyle 5$ days

Work completed: $\displaystyle 5 \times 9 = 45$

Remaining work: $\displaystyle 100 - 45 = 55$

A will finish in: $\displaystyle \frac{55}{5} = 11\:\underline{Ans}$

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