Multiple choice

Raju and Kamal decided to do a given task together but by doing it on alternate days. Raju alone could do the task in 15 days and Kamal alone could do the task in 20 days. When they started working together alternately, Raju said that he would start from the first day. In how many days would the task get finished?

  1. 11

  2. 13

  3. 15

  4. 17

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Raju's rate = 1/15, Kamal's rate = 1/20. In a 2-day cycle, they do 1/15 + 1/20 = 7/60 of the work. In 8 cycles (16 days), they do 8 * (7/60) = 56/60. Remaining work = 4/60 = 1/15. On day 17, Raju works and completes 1/15. Total = 17 days.

AI explanation

Using the least common multiple method, let the total work be 60 units, making Raju's daily work 4 units and Kamal's daily work 3 units. Working on alternate days starting with Raju, their 2-day combined work cycle yields 7 units. After 6 such cycles (12 days), they complete 42 units, leaving 18 units of work; Raju does 4 units on day 13 (leaving 14), Kamal does 3 on day 14 (leaving 11), Raju does 4 on day 15 (leaving 7), Kamal does 3 on day 16 (leaving 4), and Raju works on day 17 to finish the last 4 units, totaling 17 days.

Keep practicing — related questions