Multiple choice

Find the correct relationship between given quantities. Mahesh can complete a piece of work in 60 days whereas Kavya and Sarita working together can complete it in 15 days. When Mahesh and Sarita alternately work for a day each the work gets completed in 40 days. Quantity 1: No. of days in which Kavya will complete the work. Quantity 2: No. of days in which Sarita will complete the work.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relationship can be established

Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Mahesh: 60 days. Kavya+Sarita: 15 days. Mahesh+Sarita (alternate days): 40 days. Let Kavya take k days, Sarita take s days. Kavya+Sarita combined rate: 1/15. Mahesh's rate: 1/60. When working alternate days, in 40 days they complete 40*(1/60 + 1/s)/2 = 40/120 + 20/s. This equals 1. So 1/3 + 20/s = 1, giving s = 30. So Sarita takes 30 days. Then Kavya takes 1/(1/15 - 1/30) = 30 days. Both take 30 days, so Kavya = Sarita, meaning Quantity I = Quantity II.