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MAT Exam 2024 Paper

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Question : 79 of 150

Marks: +1, -0

The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working hours per day, 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same working 8 hours per day?

$2 \frac{1}{2}$ days
$1 \frac{1}{2}$ days
$3 \frac{2}{41}$ days
None of these

Solution:

Concept:

Convert all workers into equivalent men using the given work-time relation, then apply the work formula.

Explanation:

Given:

8

women

= 6

men

= 12

boys.

So,

12

women

= \frac{12}{8} \times 6 = 9

men.

And

12

boys

= \frac{12}{12} \times 6 = 6

men.

Therefore, total combined capacity:

12\text{ men}+12\text{ women}+12\text{ boys} = 12+9+6=27\text{ men}

For 9 men working 6 hours per day for 6 days, and 27 men working 8 hours per day:

M_1D_1T_1 = M_2D_2T_2

9 \times 6 \times 6 = 27 \times D_2 \times 8

D_2 = \frac{9 \times 6 \times 6}{27 \times 8} = \frac{3}{2}

\frac{3}{2} = 1\frac{1}{2}\text{ days}

Answer:

Option B:

1 \frac{1}{2}

days

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