Multiple choice

Passage

Directions : Study the given information and answer the following question. Reema, Mahesh and Suresh are working together as a team to complete the treasure hunt task in fun activities organised during college fest. Reema takes 5 more days than Mahesh and 9 more days than Suresh to complete the task alone. Reema and Mahesh together can complete the task in the same time as Suresh alone can.

How many days would Reema take to complete the task when she is working alone?

  1. 13 days

  2. 16 days

  3. 15 days

  4. 20 days

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M, R, S be days taken by Mahesh, Reema, and Suresh. R = M+5, R = S+9. 1/R + 1/M = 1/S. Substituting M = R-5 and S = R-9 gives 1/R + 1/(R-5) = 1/(R-9). Solving this quadratic equation: (R-5+R)/(R(R-5)) = 1/(R-9) => (2R-5)(R-9) = R^2-5R => 2R^2 - 23R + 45 = R^2 - 5R => R^2 - 18R + 45 = 0. Roots are 15 and 3. Since R must be > 9, R = 15.

AI explanation

Let Mahesh take m days to complete the task alone, so Reema takes m plus 5 days. Given that Reema takes 9 more days than Suresh, Suresh takes m minus 4 days. The problem states that Reema and Mahesh together take the same time as Suresh alone, leading to the work equation 1/(m+5) plus 1/m equals 1/(m-4). Solving this equation yields m equals 10, meaning Mahesh takes 10 days, Suresh takes 6 days, and Reema takes 10 plus 5 days, which equals 15 days.

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