A can do \(\frac{1}{4}^{\text {th}}\) of a work in 3 days and B can do \(\frac{1}{6}^{\text {th}}\) of the same work in 4 days. How much will A get if both worked together and are paid ₹18,000 in all?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ₹12,000
When two people work together for the same time, the payment is shared in the ratio of the work each does in a day, so each one’s time for the whole work is found first.
A does \(\frac{1}{4}\) of the work in 3 days, so the whole work in \(4\times3=12\) days
B does \(\frac{1}{6}\) of the work in 4 days, so the whole work in \(6\times4=24\) days
One day’s work, A : B \(\displaystyle =\frac{1}{12}:\frac{1}{24}=2:1\)
A’s share \(\displaystyle =\frac{2}{3}\times18000=12000\), that is, ₹12,000