Question : A completes 30% of a project in 30 days. He then calls in B and they together finish the remaining work in 20 days. How long would B alone take to do the whole work?
Option 1: 40 days
Option 2: 80 days
Option 3: 120 days
Option 4: 20 days
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Correct Answer: 40 days
Solution : Given: A completes 30% of a project in 30 days. Let the total work be 100 units. Since we know that, Total work = Efficiency × Time. So, A's efficiency is $\frac{30}{30}$ = 1 unit each day. After that, he calls B and the two of them complete the remaining work in 20 days. So, the work left is 70 units. Assuming that B's efficiency is $x$ units per day. So, $\frac{70}{(1+x)}=20$ ⇒ $20+20x = 70$ ⇒ $20x = 50$ ⇒ $x = 2.5$ units per day. So, if B worked by himself, it would require $\frac{100}{2.5}=40$ days Hence, the correct answer is 40 days.
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