Multiple choice

X alone can plough a field in 12 days, and Y alone can plough it in 16 days. They completed the work in 6 days with the help of Z. If the total payment for the work was Rs. 6,400, how much should Z be paid?

  1. Rs. 1,600

  2. Rs. 800

  3. Rs. 600

  4. Rs. 400

  5. na
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

X's rate = 1/12, Y's rate = 1/16. Together in 6 days: 6 * (1/12 + 1/16) = 6 * (7/48) = 7/8 of the work. Z did 1/8 of the work. Payment for Z = (1/8) * 6400 = 800.

AI explanation

Using the Least Common Multiple method, let the total work be 48 units. The daily work capacities are 4 units for X, 3 units for Y, and Z units for Z, making a combined daily capacity of 7 plus Z. Since the team finishes the 48 units in 6 days, their combined daily capacity is 8 units, meaning Z completes 1 unit daily. Z therefore contributes 6 units out of the total 48 units, so his proportional payment from the Rs. 6,400 total is 6400 multiplied by 6 divided by 48, which equals Rs. 800.

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