Multiple choice

4 men and 6 woman get Rs 1600 by doing a piece of work in 5 days. 3 men and 7 woman get Rs 1740 by doing the same work in 6 days. In how many days, 7 men and 6 woman can complete the same work getting Rs 3760?

  1. $6$ days
  2. $8$ days
  3. $10$ days
  4. $12$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be daily wage of a man, W of a woman. (4M + 6W) * 5 = 1600 => 4M + 6W = 320. (3M + 7W) * 6 = 1740 => 3M + 7W = 290. Solving: 12M + 18W = 960 and 12M + 28W = 1160. 10W = 200, W = 20. 4M + 120 = 320, 4M = 200, M = 50. For 7M + 6W: 7(50) + 6(20) = 350 + 120 = 470 per day. Days = 3760 / 470 = 8.

AI explanation

Let m be the daily wage of a man and w be the daily wage of a woman; the first statement gives the equation 5*(4m + 6w) = 1600, which simplifies to 4m + 6w = 320. The second statement gives 6*(3m + 7w) = 1740, which simplifies to 3m + 7w = 290. Solving this system yields m = 50 and w = 20; dividing the total amount of Rs 3760 by the daily wage of 7 men and 6 women ((7*50 + 6*20) = 470) gives 8 days. The correct result is 8 days.

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