Multiple choice

In how many days can the work be done by 9 men and 15 women? Statements: (I) 6 men and 5 women can complete the work in 6 days. (II) 3 men and 4 women can complete the work in 10 days. (III) 18 men and 15 women can complete the work in 2 days.

  1. Only I

  2. Only II

  3. Any two

  4. All I, II and III

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let m = one man's work per day, w = one woman's work per day. From I: 6m + 5w = 1/6. From II: 3m + 4w = 1/10. From III: 18m + 15w = 1/2. Any two equations can solve for m and w: multiply II by 2 gives 6m + 8w = 1/5, subtract from I gives 3w = 1/5 - 1/6 = 1/30, so w = 1/90. Then m = (1/10 - 4/90) ÷ 3 = 1/180. For 9 men and 15 women: 9/180 + 15/90 = 1/20 + 1/6 = 13/60, so work finishes in 60/13 ≈ 4.6 days.

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