Multiple choice

Geeta, Mina and Sunita, working together, take 4 days to finish a job. Instead, if only Geeta and Sunita take up the job, they can finish it in 15 days less than the time taken by Mina to complete the job, working alone. Mina started the job and after 2 days Geeta and Sunita joined her. Mina quit after working for 2 more days. In how many days was the job completed?

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be the time for Mina. G+S+M = 1/4. G+S = 1/(M-15). So 1/(M-15) + 1/M = 1/4. Solving M^2 - 23M + 60 = 0 gives M=20 or M=3. Since M>15, M=20. G+S = 1/5. Mina works 4 days (2+2), G+S work 2 days. Work done = 4/20 + 2/5 = 1/5 + 2/5 = 3/5. Remaining 2/5 work done by G+S in (2/5) / (1/5) = 2 days. Total time = 4 + 2 = 6 days.

AI explanation

Let the time taken by Geeta, Mina, and Sunita alone be g, m, and s days, respectively. Their combined rate is 1/g + 1/m + 1/s = 1/4. The second condition states that 1/g + 1/s = 1/(m - 15). Substituting this into the first equation gives 1/(m - 15) + 1/m = 1/4. Solving this yields the quadratic equation m^2 - 23m + 60 = 0, which factors into (m - 20)(m - 3) = 0; since m must be greater than 15, m = 20 days. Mina's efficiency is 1/20, and Geeta and Sunita's combined efficiency is 1/5. Mina works alone for 2 days, completing 2/20 = 1/10 of the job, leaving 9/10 of the job remaining. Then all three work together for 2 days, completing 2 x (1/4) = 1/2 of the job, leaving 9/10 - 1/2 = 4/10 of the job. Geeta and Sunita then work together to complete the remaining 4/10 of the job at a rate of 1/5 per day, taking (4/10) divided by (1/5) = 2 days. The total time is 2 + 2 + 2 = 6 days. The result is 6.

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