Multiple choice

Kadil, Piyush and Sachin can do a piece of work, working together, in 2 days. Kadil is 6 times as efficient as Piyush. Piyush takes 5 times the number of days as Sachin takes to do it alone. What will be the difference between the number of days taken by Piyush and Kadil?

  1. 12 days

  2. 20 days

  3. 10 days

  4. 4 days

  5. 8 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Sachin take S days. Piyush takes 5S days. Kadil is 6 times as efficient as Piyush, so Kadil takes (5S)/6 days. Together: 1/S + 1/(5S) + 6/(5S) = 1/2. (5+1+6)/(5S) = 1/2. 12/(5S) = 1/2. 5S = 24, S = 4.8. Piyush = 5 * 4.8 = 24 days. Kadil = 24/6 = 4 days. Difference = 24 - 4 = 20 days.

AI explanation

Let Piyush's efficiency be 1 unit per day, making Kadil's efficiency 6 units per day. If Piyush takes 5 times the days Sachin takes, Sachin's efficiency is 5 times Piyush's, so Sachin's efficiency is 5 units per day. Their combined efficiency is 12 units per day (6 plus 1 plus 5), and since they complete the work in 2 days, the total work is 24 units (12 multiplied by 2). Kadil takes 4 days (24 divided by 6) and Piyush takes 24 days (24 divided by 1). The difference between the number of days taken by Piyush and Kadil is 20 days (24 minus 4).

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