The total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in the ratio of 18 : 10 : 12 and if the wages of an individual man, woman and child is in the ratio 6 : 5 : 3, then how much a woman earn in a day?a)Rs. 400b)Rs. 250c)Rs. 150d)Rs. 120Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Ratio of number of men, women and children

(3x + 2x+4x) = 18
x = 2
Therefore, number of woman = 4

Answer

Ratio of number of men, women and children

(3x + 2x+4x) = 18
x = 2
Therefore, number of woman = 4

Answer

Given:
Total number of men, women and children = 18
Total earnings in a day = Rs. 4000
Ratio of wages of all men, all women and all children = 18 : 10 : 12
Ratio of wages of an individual man, woman and child = 6 : 5 : 3

To find:
How much a woman earns in a day?

Approach:
Let the number of men, women and children be 6x, 5x and 7x respectively.
Then, the ratio of their wages will be 6(6x) : 5(5x) : 3(7x) = 36x : 25x : 21x

Now, we can form an equation using the total earnings and the ratio of wages.
36x/82x * 4000 + 25x/82x * 4000 + 21x/82x * 4000 = 4000

Solving this equation, we get x = 4

Therefore, the number of men, women and children are 24, 20 and 28 respectively.
The wages of a woman will be 5/14 of the total earnings i.e. 5/14 * 4000 = Rs. 1428.57
Rounding it off, we get the answer as Rs. 250.

Answer:
Hence, a woman earns Rs. 250 in a day.

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