Hema can type a report in 15 days and Isha can type it in 20 days. They type together for 5 days; then Hema stops, and Isha types the rest of the report alone. In how many days from the start is the report completed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(13\frac{1}{3}\)
Find the part typed together, then the time Isha needs for what is left, and add the two periods.
One day together \(\displaystyle =\frac{1}{15}+\frac{1}{20}=\frac{4+3}{60}=\frac{7}{60}\)
In 5 days together \(\displaystyle =\frac{35}{60}\); left \(\displaystyle =\frac{25}{60}\)
Isha alone \(\displaystyle =\frac{25}{60}\times20=\frac{25}{3}=8\frac{1}{3}\) days
Total \(\displaystyle =5+8\frac{1}{3}=13\frac{1}{3}\) days
The report is completed in \(13\frac{1}{3}\) days.
Why the other options are incorrect
Option (1) \(8\frac{1}{3}\) — Incorrect. This is only Isha’s time after Hema stops; the first 5 days are left out.
Option (2) 12 — Incorrect. Isha would have only 7 days, typing \(\frac{7}{20}=\frac{21}{60}\), less than the \(\frac{25}{60}\) left.
Option (4) \(14\frac{1}{2}\) — Incorrect. Isha would type for \(9\frac{1}{2}\) days, more than she needs.