Multiple choice

Women, men and children are employed to do a piece of work in the proportion 3 : 2 : 1 and their wages are in the proportion 5 : 3 : 2. When 90 women are employed, total daily wages of all amounts to Rs. 11,730. Find the daily wage of a woman.

  1. Rs. 65

  2. Rs. 85

  3. Rs. 80

  4. Rs. 60

  5. None of these
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B Correct answer
Explanation

Let the number of workers be 3x, 2x, x for women, men, children. Given 3x = 90, so x = 30. Total workers: 90 women, 60 men, 30 children. Let wages be 5y, 3y, 2y. Total wage = 90(5y) + 60(3y) + 30(2y) = 450y + 180y + 60y = 690y. 690y = 11730, so y = 17. A woman's daily wage is 5y = 5 * 17 = 85.

AI explanation

Using the given proportion of 3:2:1 for 90 women, the number of men is 60 and the number of children is 30. Let the daily wages per woman, man, and child be 5x, 3x, and 2x respectively. The total daily wage equation is 90 multiplied by 5x plus 60 multiplied by 3x plus 30 multiplied by 2x, which equals 11,730. This simplifies to 450x plus 180x plus 60x equals 11,730, or 690x equals 11,730. Solving for x gives x equals 17, making the daily wage of a woman 5x, which is 85 rupees.

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