Question : J1 can do a piece of work alone in 10 days, J2 can do the same work alone in 12 days, while J3 can do it alone in 15 days. They work together and complete the work, and receive a total of INR 2,250 for doing the work. What is the difference in the shares of J1 and J3?
Option 1: INR 450
Option 2: INR 400
Option 3: INR 300
Option 4: INR 350
Correct Answer: INR 300
Solution :
LCM of 10. 12 and 15 is 60
Total work = 60
Efficiency of J
1
= $\frac{60}{10}=6$
Efficiency of J
2
= $\frac{60}{12}=5$
Efficiency of J
3
= $\frac{60}{15}=4$
The ratio of their efficiencies = 6 : 5 : 4
Amount received = INR 2250
Share of J
1
= $\frac{2250}{15}\times6=900$
Share of J
2
= $\frac{2250}{15}\times5=750$
Share of J
3
= $\frac{2250}{15}\times4=600$
The difference in the shares of J
1
and J
3
= 900 – 600 = 300
Hence, the correct answer is INR 300.
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