A and B get a wage of Rs. 1200 for a work. A can do it in 15 days and B can do it in 12 days. With the help of C, they finish it in 5 days. What is C's wage?
Answer: B
Wages are shared in the ratio of work done. (A+B+C)'s 1 day work = 1/5. A's work=1/15, B's work=1/12. C's 1 day work = \(1/5 - (1/15+1/12) = 1/5 - (4+5)/60 = 1/5 - 9/60 = 12/60-9/60=3/60=1/20\). Ratio of work A:B:C = 1/15 : 1/12 : 1/20. Multiplying by 60 gives 4:5:3. C's share = \(\frac{3}{4+5+3} \times 1200 = \frac{3}{12} \times 1200 = 300\). Wait, C's work is 1/20. So C's share is 1/4 of A's. Let's re-calculate. A's share is prop to 1/15. B's to 1/12. C's to 1/20. Ratio of work A:B:C is 4:5:3. C's share is 3/12 of total wage = 300. Why is the answer 240? Let me check again. A=1/15, B=1/12, A+B+C=1/5. A's work in 5 days = 5/15=1/3. B's work in 5 days = 5/12. C's work in 5 days = 1 - (1/3+5/12) = 1 - (4+5)/12 = 1 - 9/12 = 3/12 = 1/4. Ratio of work done A:B:C = 1/3:5/12:1/4 = 4:5:3. Sum is 12. C's share is (3/12)*1200=300. I consistently get 300. The answer key is wrong. I will correct it.