A, B and C worked together for 5 days to build a wall and then B left the work. A and C together finished the remaining work in 5 days. In how many days can A and C working together finish building the whole wall if B alone can do it in 25 days?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(12\displaystyle\frac{1}{2}\)
Work is added through daily rates, the part of the wall each worker builds in a day. Let A and C together build \(x\) of the wall in a day; B alone builds \(\displaystyle\frac{1}{25}\) of it.
First 5 days (A, B and C): \(\displaystyle 5\left(x+\frac{1}{25}\right)=5x+\frac{1}{5}\)
Next 5 days (A and C): \(5x\)
The whole wall: \(\displaystyle 5x+\frac{1}{5}+5x=1\)
\(\displaystyle 10x=\frac{4}{5}\), so \(\displaystyle x=\frac{2}{25}\)
A and C together: \(\displaystyle\frac{25}{2}=12\frac{1}{2}\) days
Shortcut:
B worked only 5 of his 25 days, so he built \(\displaystyle\frac{1}{5}\) of the wall
A and C, working all 10 days, built the other \(\displaystyle\frac{4}{5}\), so the whole wall would take them \(\displaystyle 10\times\frac{5}{4}=12\frac{1}{2}\) days