Anil paints one-fourth of a boundary wall in 2 days, and Bimal paints two-fifths of the same wall in 8 days. They paint together for 4 days, and then Anil leaves. How many more days will Bimal take to finish painting the wall alone?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6
From the part painted in a given number of days we get each painter’s time for the whole wall.
Anil: \(\frac{1}{4}\) in 2 days, so the whole wall in \(2\times4=8\) days
Bimal: \(\frac{2}{5}\) in 8 days, so the whole wall in \(\displaystyle 8\times\frac{5}{2}=20\) days
One day together \(\displaystyle =\frac{1}{8}+\frac{1}{20}=\frac{5+2}{40}=\frac{7}{40}\)
In 4 days together \(\displaystyle =\frac{28}{40}=\frac{7}{10}\); left \(\displaystyle =\frac{3}{10}\)
Bimal alone \(\displaystyle =\frac{3}{10}\times20=6\) days
Bimal takes 6 more days.
Why the other options are incorrect
Option (1) 5 — Incorrect. In 5 days Bimal paints only \(\frac{5}{20}=\frac{1}{4}\), less than the \(\frac{3}{10}\) left.
Option (3) 8 — Incorrect. 8 days is Anil’s time for the whole wall; Bimal needs only 6 days for \(\frac{3}{10}\).
Option (4) 12 — Incorrect. In 12 days Bimal would paint \(\frac{12}{20}=\frac{3}{5}\), twice what is left.