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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 xx days. B works right till the end, so B works for x+20x+20 days.

Using rate×time=work done\text{rate}\times\text{time}=\text{work done}:

PersonRate (work per day)Time (days)Work done
A140\dfrac{1}{40}xxx40\dfrac{x}{40}
B150\dfrac{1}{50}x+20x+20x+2050\dfrac{x+20}{50}

The whole job counts as 1, so

x40+x+2050=1\dfrac{x}{40}+\dfrac{x+20}{50}=1

Multiply every term by 200:

5x+4(x+20)=2005x+4(x+20)=200

⇒5x+4x+80=200\Rightarrow 5x+4x+80=200

⇒9x=120\Rightarrow 9x=120

⇒x=1209=403=1313\Rightarrow x=\dfrac{120}{9}=\dfrac{40}{3}=13\dfrac{1}{3}

A left after 131313\dfrac{1}{3} days.

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