Multiple choice

To complete a certain piece of work, the time taken by A and C is 2 days more than that taken by A, B and C. The time taken by B and C is 150% more than that taken by A, B and C to complete the work. A, B and C together completed the work earning a total of Rs.9860 in which the share of C is Rs.1479. How many days did A, B, C take to complete the work?

  1. 5 1/3

  2. 7 1/2

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let T be the time taken by A, B, C. A+C = T+2, B+C = 2.5T. Using work rates: 1/(T+2) + 1/(2.5T) - 1/T = 1/C. Also, C's share of earnings is proportional to his work rate. Solving these equations yields T = 6.

AI explanation

Let the time taken by A, B and C together be T days, making their combined rate 1/T. The rate of A and C is 1/(T plus 2) and the rate of B and C is 1/(2.5T). Since A's rate is the difference between the total rate and C's rate, and B's rate is the difference between the total rate and A's rate, the ratio of their daily work is A equal to 1.5 divided by T squared, and B equal to 0.55 divided by T squared. The ratio of shares of A, B and C is 30 to 11 to 19, and since C's share of Rs 1479 corresponds to 19 parts out of the total 60 parts, the total earnings for T days of work are Rs 4680. Dividing the total earnings by the combined daily wage of Rs 780 gives T equals 6.

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