Kavya can paint a boundary wall in 12 days and Leena can paint it in 18 days. They paint together for 3 days; then Kavya stops, and Leena paints the rest of the wall alone. In how many days from the start is the wall completed?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(13\frac{1}{2}\)
Find the part painted together, then the time Leena needs for what is left, and add the two periods.
One day together \(\displaystyle =\frac{1}{12}+\frac{1}{18}=\frac{3+2}{36}=\frac{5}{36}\)
In 3 days together \(\displaystyle =\frac{15}{36}\); left \(\displaystyle =\frac{21}{36}\)
Leena alone \(\displaystyle =\frac{21}{36}\times18=\frac{21}{2}=10\frac{1}{2}\) days
Total \(\displaystyle =3+10\frac{1}{2}=13\frac{1}{2}\) days
The wall is completed in \(13\frac{1}{2}\) days.
Why the other options are incorrect
Option (2) \(10\frac{1}{2}\) — Incorrect. This is only Leena’s time after Kavya stops; the first 3 days are left out.
Option (3) 12 — Incorrect. Leena would have only 9 days, painting \(\frac{9}{18}=\frac{18}{36}\), less than the \(\frac{21}{36}\) left.
Option (4) 15 — Incorrect. Leena would paint for 12 days, \(\frac{12}{18}=\frac{24}{36}\), more than the \(\frac{21}{36}\) left.