Multiple choice

A can do a piece of work in 15 days while B can do it in 20 days. They work together for 5 days and remaining work is completed by C in 10 days. If the total amount received for the whole work is $6000, how should the money be divided among them?

  1. $2000, $1500, $2500
  2. $1800, $2800, $800
  3. $2000, $1400, $1000
  4. $900, $1600, $1400
  5. $1500, $2000, $2500
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate is 1/15, B's is 1/20. Together they do (1/15 + 1/20) = 7/60 per day. In 5 days, they do 35/60 = 7/12 of the work. C does the remaining 5/12 in 10 days, so C's rate is (5/12)/10 = 1/24. The ratio of work done is A: 5/15 = 1/3, B: 5/20 = 1/4, C: 5/12. Ratio is 4:3:5. Dividing 6000 in this ratio: A = 2000, B = 1500, C = 2500.

AI explanation

A and B together complete 5 times (1/15 + 1/20) of the work in 5 days, which equals 35/60 or 7/12 of the work. This leaves 5/12 of the work for C. Since wages are divided in the proportion of work done, A gets 1/3 (5/15) of \$6000, B gets 1/4 (5/20) of \$6000, and C gets 5/12 of \$6000. The final distribution is \$2000, $1500, and $2500 respectively.

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