Multiple choice

'A' takes 10 days less than the time taken by 'B' to finish a piece of work. If 'A' and 'B' together can finish the work in 12 days, find the time taken by B to finish the work.

  1. 24 days

  2. 30 days

  3. 32 days

  4. 28 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B take x days, A takes x-10 days. Combined rate: 1/x + 1/(x-10) = 1/12. Solving x^2 - 34x + 120 = 0 gives (x-30)(x-4) = 0. Since x must be > 10, x = 30.

AI explanation

Let B take x days to finish the work, making A's time (x - 10) days. Since their combined time is 12 days, the equation for their combined rate is 1/x + 1/(x - 10) = 1/12. Multiplying by the common denominator of 12x(x - 10) yields 12(x - 1) + 12x = x^2 - 10x, which simplifies to x^2 - 34x + 120 = 0. Factoring this quadratic equation gives (x - 30)(x - 4) = 0, and because A's time of x - 10 must remain positive, x is 30 days.

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