‘A’ can do a piece of work in 10 days while B alone can do it in 15 days. They work together for 5 days and the rest of work is done by ‘C’ in 24 days. If they get Rs 1614 for the whole work, what is the share of ‘C’.

A's rate = 1/10 per day, B's rate = 1/15 per day. Together in 5 days they complete 5(1/10+1/15) = 5(1/6) = 5/6 of work. Remaining 1/6 done by C in 24 days, so C's rate = 1/144 per day. Total rate of all three = 1/10+1/15+1/144. C's share of wage = (C's rate)/(combined rate) × 1614 = 1614/24 = 67.25. However, looking at the options, 269 Rs equals 4 × 67.25, suggesting C's work share is 1/6 of total, so wage = (1/6)/(1) × 1614 = 269. Answer C is correct.