Lata can weave a carpet in 24 days and Mohan can weave the same carpet in 36 days. They begin weaving it together. After some days Lata stops, and Mohan completes the carpet by himself in another 6 days. For how many days did Lata work on the carpet?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12
The part done by the two together plus the part Mohan does alone makes up the whole carpet.
Mohan alone in the last 6 days: \(\displaystyle \frac{6}{36}=\frac{1}{6}\) of the carpet
Part done together \(\displaystyle =1-\frac{1}{6}=\frac{5}{6}\)
One day’s work together \(\displaystyle =\frac{1}{24}+\frac{1}{36}=\frac{3+2}{72}=\frac{5}{72}\)
Days together \(\displaystyle =\frac{5}{6}\div\frac{5}{72}=\frac{5}{6}\times\frac{72}{5}=12\)
Lata worked for 12 days.
Why the other options are incorrect
Option (1) 9 — Incorrect. In 9 days together they weave \(\frac{45}{72}=\frac{5}{8}\); with Mohan’s \(\frac{1}{6}\) the carpet is still not finished.
Option (2) 10 — Incorrect. In 10 days together they weave \(\frac{50}{72}\), and \(\frac{50}{72}+\frac{12}{72}=\frac{62}{72}\), less than the whole.
Option (4) 15 — Incorrect. In 15 days together they weave \(\frac{75}{72}\), more than the whole carpet, and nothing would be left for Mohan.