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: C
Since they all work for the same number of days (5 days), their wages will be in the ratio of their one-day's work (efficiency).
A's 1-day work = 1/15. B's 1-day work = 1/12. (A+B+C)'s 1-day work = 1/5.
C's 1-day work = (A+B+C)'s work - (A's work + B's work) = \(1/5 - (1/15 + 1/12) = 1/5 - (4+5)/60 = 1/5 - 9/60 = 12/60 - 9/60 = 3/60 = 1/20\).
The ratio of their efficiencies A:B:C is \(1/15 : 1/12 : 1/20\). To simplify, multiply by the LCM of 15, 12, 20, which is 60. Ratio = 4:5:3. The sum of ratios is 12.
C's wage = \(\frac{3}{12} \times 1200 = \frac{1}{4} \times 1200 = 300\). C's wage is Rs. 300.