Multiple choice

X can do a piece of work in $8$ days and Y in $12$ days. When Z joined them, they completed the work in $3$ days. If the total money received for the work was $Rs. 400,$ what would be the share of X, based upon his proportionate output?

  1. $Rs. 200$
  2. $Rs. 160$
  3. $Rs. 150$
  4. $Rs. 170$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work rates: X=1/8, Y=1/12. Together in 3 days: 3(1/8 + 1/12 + Z) = 1. 3(5/24 + Z) = 1, so 5/24 + Z = 1/3, Z = 8/24 - 5/24 = 3/24 = 1/8. Since X and Z have the same rate (1/8), they do equal work. Total work is 3 days, X does 3/8 of the work. Share = (3/8) * 400 = 150.

AI explanation

Using the LCM method to find their combined efficiency, let the total work be the least common multiple of 8 and 12 days, which is 24 units. X completes 24 units in 8 days, so X's efficiency is 3 units per day. Y completes 24 units in 12 days, so Y's efficiency is 2 units per day. Since Z joined them and we are given they all finish the work in 3 days, Z's efficiency plus X and Y's efficiency equals 8 units per day, meaning Z's efficiency is 3 units per day. The ratio of efficiencies for X, Y, and Z is 3:2:3. Based on this 3/8 proportion of the total Rs. 400, X's share is 3/8 times 400, which equals Rs. 150.

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