Multiple choice

Rajeev alone can do a certain work in 6 days less than the time that Sanjeev alone takes to complete it. They started the work together, but after 4 days, Sanjeev leaves. If Rajeev completes the remaining work in 3.5 more days, then find the time that Sanjeev alone takes to complete the entire work. It is given that in the entire process, Rajeev completed 75% of the work.

  1. 12

  2. 16

  3. 18

  4. 22
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Sanjeev take S days, Rajeev takes S-6 days. Rates are 1/(S-6) and 1/S. They work together for 4 days, then Rajeev works for 3.5 more. Total work for Rajeev = 4/(S-6) + 3.5/(S-6) = 7.5/(S-6). Given this is 75% of the work, 7.5/(S-6) = 0.75, so S-6 = 10, S = 16.

AI explanation

Let the time taken by Sanjeev to complete the work be x days, so the time taken by Rajeev is x minus 6 days. The combined work rate of Sanjeev and Rajeev is 1 divided by x plus 1 divided by (x minus 6). Working together for 4 days, they complete 4 times this combined rate. Rajeev then works alone for 3.5 days, completing 3.5 divided by (x minus 6) of the work. The total work done by Rajeev is his work during the 4 days plus his 3.5 days alone, which equals 75 percent of the total work. This gives the equation 4 divided by (x minus 6) plus 3.5 divided by (x minus 6) equals 3/4. Combining the terms gives 7.5 divided by (x minus 6) equals 3/4. Solving this yields x minus 6 equals 10, so x equals 16. The correct answer is 16.

Keep practicing — related questions