Multiple choice

Two person A and B can complete a work in 20 and 30 days respectively. With the help of C they can finish the work together in 5 days. Find the time required to complete the work by only D who is 50% more efficient than C?

  1. $\(\frac{120}{7}\)$
  2. $\(\frac{40}{7}\)$
  3. $18$
  4. $20$
  5. $36$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/20 work/day, B's rate = 1/30 work/day. Combined rate of A+B+C = 1/5 work/day. So C's rate = 1/5 - (1/20 + 1/30) = 1/5 - 5/60 = 12/60 - 5/60 = 7/60 work/day. D is 50% more efficient than C, so D's rate = 1.5 × (7/60) = 10.5/60 = 7/40 work/day. Time for D alone = 1 / (7/40) = 40/7 days.

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