Question : K1 can do a piece of work alone in 4 days, K2 can do the same work alone in 8 days, while K3 can do it alone in 32 days. They work together to complete the work and receive a total of Rs. 3,900 as payment for doing the work. What is the share of the person who received the maximum amount?
Option 1: Rs. 1,200
Option 2: Rs. 2,400
Option 3: Rs. 2,000
Option 4: Rs. 1,600
Correct Answer: Rs. 2,400
Solution :
Let the rates at which K1, K2, and K3 work as R1, R2, and R3 respectively.
K1 can do the work alone in 4 days, R1 = $\frac{1}{4}$
K2 can do the work alone in 8 days, R2 = $\frac{1}{8}$
K3 can do the work alone in 32 days, R3 = $\frac{1}{32}$
The total rate when they work together = R1 + R2 + R3 = $\frac{1}{4} + \frac{1}{8} + \frac{1}{32} = \frac{13}{32}$
So, the share of each person is proportional to their rate of work.
Share = $\frac{\text{Individual rate}}{\text{ Total rate}}$ × Total payment
The share of K1 = $\frac{R1}{R1+R2+R3} \times 3900 = \frac{1}{4}×\frac{32}{13}\times 3900 =2400$
The share of K2 = $\frac{R2}{R1+R2+R3}\times 3900 = \frac{1}{8}×\frac{32}{13}\times 3900 =1200$
The share of K3 = $\frac{R3}{R1+R2+R3}\times 3900 = \frac{1}{32}×\frac{32}{13}\times 3900 =300$
The share of the person who received the maximum amount is Rs. 2,400.
Hence, the correct answer is Rs. 2,400.
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