Multiple choice

Working at 20% more efficiency, A can complete a work in 3 days less, whereas, working at 11⅑% more efficiency, A and B together can complete the same work in 1 day less. If A, B and C, working together, can complete the same work in 6 days, and they are paid a total of ₹33,000 for the completion of the work, what'll be the share of C in it?

  1. ₹13,200

  2. ₹16,500

  3. ₹14,400

  4. None of the above
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A Correct answer
Explanation

Let A's efficiency be a. 1.2a * (T-3) = a * T -> 1.2T - 3.6 = T -> 0.2T = 3.6 -> T = 18 days. A's rate = 1/18. A+B together at 11.11% (1/9) more efficiency: (1+1/9) * (A+B) * (T-1) = 1. (10/9) * (A+B) * 17 = 1. (A+B) = 9/170. B = 9/170 - 1/18 = (81-85)/1530 = -4/1530. This implies the problem constraints are inconsistent.

AI explanation

Let A take A days to complete the work alone, and A and B together take T days to complete the work. Increasing efficiency by 20% reduces the time taken by a factor of 1.2, giving A x 1.2 = A - 3, which yields A = 18 days. An 11 1/9% efficiency increase reduces time by a factor of 1.111..., giving T x 1.111... = T - 1, which yields T = 10 days. Since A, B, and C finish the work in 6 days, their total efficiency is 1/6 per day; A's efficiency is 1/18, B's efficiency is 1/10 - 1/18 = 2/45, and C's efficiency is 1/6 - 1/18 - 2/45 = 2/15. C's proportion of the total work is (2/15) divided by (1/6), which equals 12/15 or 2/5, meaning C's share of the 33000 payment is 2/5 x 33000 = 13200. The share of C is Rs. 13,200.

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