Multiple choice

A can do a piece of work in 10 days and B in 12 days. With help of C, they finish the work in 4 days. In how many days C alone can do the same work?

  1. 12

  2. 15

  3. 18

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate is 1/10, B's is 1/12. Together with C, their rate is 1/4. C's rate = 1/4 - (1/10 + 1/12) = 1/4 - (6/60 + 5/60) = 1/4 - 11/60 = 15/60 - 11/60 = 4/60 = 1/15. Thus, C takes 15 days.

AI explanation

Using the fractions method for Time and Work, A's one day work is one tenth and B's one day work is one twelfth. Their combined one day work with C is one fourth, so C's one day work is one fourth minus one tenth minus one twelfth. Finding a common denominator of sixty, this gives fifteen minus six minus five over sixty, which equals four sixtieths or one fifteenth. Therefore, C alone can do the work in 15 days.

Keep practicing — related questions