Multiple choice

A can complete a piece of work in 9 days, while B can complete the same work in 12 days. A and B charged Rs. 5,400 to complete the work. With the help of C, they all completed the work in 4 days. Statement I: C can complete the work alone in 18 days. Statement II: C's share in the completed work is Rs. 800. In the light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.

  5. NA
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/9, B's rate = 1/12. (A+B+C) rate = 1/4. C's rate = 1/4 - 1/9 - 1/12 = (9-4-3)/36 = 2/36 = 1/18. So C completes work in 18 days (Statement I is true). C's share = (1/18) * 5400 = 300 (Statement II is false).

AI explanation

We find the total work by using the least common multiple of the days given, which is 36 units, making A's rate 4 units per day and B's rate 3 units per day. Working together for 4 days, A and B complete 28 units, leaving 8 units of work for C, which means C's rate is 2 units per day and C would take 18 days to complete the work alone, making Statement I true. Since the ratio of their work efficiencies is 4:3:2, C's share of the total wage is 2/9 of Rs. 5,400, which calculates to Rs. 1,200, proving Statement II is false. The result is that Statement I is true, but Statement II is false.

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