Multiple choice

$A$ alone can do a piece of work in $6$ days and $B$ alone in $8$ days. $A$ and $B$ undertook to do it for $Rs. 3200.$ With the help of $C,$ they completed the work in $3$ days. How much is to be paid to $C$?

  1. $300$
  2. $400$
  3. $600$
  4. $800$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's daily work is 1/6 and B's is 1/8. In 3 days, A does 3/6 = 1/2 and B does 3/8 of the work. Together they do 1/2 + 3/8 = 7/8 of the work, leaving 1/8 for C. Since C does 1/8 of the total work, C's share is 1/8 of 3200, which is 400.

AI explanation

The total work is the least common multiple of 6 and 8, which is 24 units, making the daily work units of A, B and C equal to 4, 3 and 1 respectively. Since the wages are distributed in proportion to the daily work units, the ratio of their shares is 4 to 3 to 1, making a total of 8 parts. C's share is 1 part out of 8, so the payment is 3200 multiplied by 1 over 8, resulting in 400.

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