Arun cooks as fast as Bala and Chetan put together. Arun and Bala, working together, can cook the meals for a school function in 8 days, while Chetan alone needs 40 days for the same meals. How many days would Bala alone need?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20 days
Work in one day is the rate. Arun’s rate equals Bala’s rate plus Chetan’s rate.
Let Bala and Chetan do \(B\) and \(C\) of the work in a day. Arun does \(B+C\)
Arun and Bala together: \(\displaystyle (B+C)+B=2B+C=\frac{1}{8}\)
Chetan alone: \(\displaystyle C=\frac{1}{40}\)
\(\displaystyle 2B=\frac{1}{8}-\frac{1}{40}=\frac{5-1}{40}=\frac{4}{40}\), so \(\displaystyle B=\frac{2}{40}=\frac{1}{20}\)
Bala alone needs 20 days.
Why the other options are incorrect
Option (1) 10 days — Incorrect. Then \(2B+C=\frac{2}{10}+\frac{1}{40}=\frac{9}{40}\), which is more than \(\frac{1}{8}=\frac{5}{40}\).
Option (2) 16 days — Incorrect. Then \(2B+C=\frac{2}{16}+\frac{1}{40}=\frac{6}{40}\); the pair would finish in less than 8 days.
Option (4) 40 days — Incorrect. Then \(2B+C=\frac{2}{40}+\frac{1}{40}=\frac{3}{40}\), less than \(\frac{5}{40}\).