Multiple choice

Some men can do a piece of work in a certain number of days working for a certain number of hours a day. If the number of men, their efficiency and the working hours per day, all are increased by 25%, they complete their work in 61 days less time than estimated. What is the estimated number of days?

  1. 125

  2. 120

  3. 100

  4. 80

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M, E, H, D be men, efficiency, hours, and days. Work = M*E*H*D. New work = (1.25M)(1.25E)(1.25H)(D-61). Since work is constant: M*E*H*D = 1.25^3 * M*E*H(D-61). D = 1.953125 * (D-61). D = 1.953125D - 119.14. 0.953125D = 119.14, D = 125.

AI explanation

Using the formula M1 * D1 * H1 * E1 = M2 * D2 * H2 * E2, the initial number of men, hours, and efficiency are all increased by 25%, making the new factors 1.25 times the original. The equation becomes M * D * H * E = (1.25M) * D2 * (1.25H) * (1.25E), which simplifies to D = 1.953125 * D2. It is given that D - D2 = 61, so substituting D2 = D / 1.953125 gives D - (D / 1.953125) = 61. Solving this gives D = 125 days.

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