Multiple choice

Two man undertook to do a job for Rs.$1400$. One of them can do it alone in $7$ days and the other in $8$ days. With the assistance of a boy, they together completed the work in $3$ days. How much money did the boy get ?

  1. Rs. $265$
  2. Rs. $275$
  3. Rs. $285$
  4. Rs. $295$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: A = 1/7, B = 1/8. Together A+B = 15/56. In 3 days, they do 3 * 15/56 = 45/56 of the work. The boy does 1 - 45/56 = 11/56 of the work. Boy's share = (11/56) * 1400 = 11 * 25 = 275.

AI explanation

Using the least common multiple method, let the total work be 168 units, as it is divisible by 7, 8, and 3. The first man does 168 divided by 7, or 24 units per day, and the second man does 168 divided by 8, or 21 units per day. Together, they complete 45 units per day, but with the boy's help, the team completes 168 divided by 3, or 56 units per day. This means the boy contributes 56 minus 45, which is 11 units per day. The boy's share of the total work is 11 out of 56, so his payment is 11/56 multiplied by Rs. 1400, resulting in Rs. 275.

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