Multiple choice

Arjun and Meera together can complete a certain assignment in 36 days. On a day when Arjun works at only 60% of his usual capacity, Meera needs to work at 160% of her normal rate to keep their combined daily output unchanged. How many days would the quicker of the two take to finish the assignment working alone?

  1. 30

  2. 45

  3. 60

  4. 75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and M be rates. (A+M)*36 = 1. (0.6A + 1.6M)*36 = 1. So A+M = 0.6A + 1.6M => 0.4A = 0.6M => A = 1.5M. Substitute into A+M = 1/36: 2.5M = 1/36 => M = 1/(36*2.5) = 1/90. A = 1.5/90 = 1/60. The quicker one is A, taking 60 days.

AI explanation

Let the one day work of Arjun be A and the one day work of Meera be M, so their normal combined rate is A plus M equals 1/36. When Arjun works at 60 percent capacity and Meera works at 160 percent capacity, the equation is 0.60A plus 1.60M equals 1/36. Equating the two expressions gives A plus M equals 0.60A plus 1.60M, which simplifies to 0.40A equals 0.60M, or A equals 1.5M. Substituting this into the first equation yields 2.5M equals 1/36, meaning M equals 1/90 and Meera takes 90 days. Substituting M back into the equation gives A equals 1/60, so Arjun takes 60 days, making him the quicker worker.

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