Multiple choice

10 men and 18 boys together can complete a work in 4 days . 6 men and 4 boys can complete the same work in 10 days .find the ratio of efficiency of 5 men and 8 boys ?

  1. 1:1

  2. 2:3

  3. 3:2

  4. 4:5

  5. 5:6
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A Correct answer
Explanation

Let 1 man's work per day = m and 1 boy's work per day = b. From first condition: 10 men and 18 boys complete work in 4 days, so 40m + 72b = 1 (total work). From second condition: 6 men and 4 boys complete work in 10 days, so 60m + 40b = 1. Solving these equations: multiply first by 3 (120m + 216b = 3) and second by 2 (120m + 80b = 2). Subtract: 136b = 1, so b = 1/136. Then 60m = 1 - 40/136 = 96/136, giving m = 8/(5×136). Efficiency of 5 men = 5m = 40/(5×136) = 8/136. Efficiency of 8 boys = 8b = 8/136. Ratio is 1:1.

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