A and B can do a piece of work in 40 days and 50 days, respectively. Both begin doing the work together but after certain time A leaves. Then, B finishes the remaining work in 20 days. After how many days did A leave?
Solution
✅ Correct Option: 3
Let A leave after $x$ days. B works right till the end, so B works for $x+20$ days. Using $\text{rate}\times\text{time}=\text{work done}$: | Person | Rate (work per day) | Time (days) | Work done | |---|---|---|---| | A | $\dfrac{1}{40}$ | $x$ | $\dfrac{x}{40}$ | | B | $\dfrac{1}{50}$ | $x+20$ | $\dfrac{x+20}{50}$ | The whole job counts as 1, so $\dfrac{x}{40}+\dfrac{x+20}{50}=1$ Multiply every term by 200: $5x+4(x+20)=200$ $\Rightarrow 5x+4x+80=200$ $\Rightarrow 9x=120$ $\Rightarrow x=\dfrac{120}{9}=\dfrac{40}{3}=13\dfrac{1}{3}$ A left after $13\dfrac{1}{3}$ days.