Multiple choice

$A$ can do a certain work in the same time in which $B$ and $C$ together can do it. If $A$ and $B$ together could do it in $10$ days and $C$ alone in $50$ days, then $B$ alone could do it in

  1. $15$ days
  2. $20$ days
  3. $25$ days
  4. $30$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A = B + C (in terms of work rate). A + B = 1/10, C = 1/50. Since A = B + C, substitute A: (B + C) + B = 1/10 => 2B + 1/50 = 1/10 => 2B = 5/50 - 1/50 = 4/50 = 2/25. So B = 1/25. B takes 25 days.

AI explanation

Since A's rate equals B and C's combined rate, the total work rate of A, B, and C is twice A's rate, meaning the whole job would take A 20 days to complete. Given that A and B together take 10 days, their combined rate is 1/10, and subtracting A's rate of 1/20 leaves B's rate as 1/20. Therefore, B alone could do it in 25 days.

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