Question

Q59. If 10 men or 15 women can do a piece of work in 36 days, then how many days will 12 men and 18 women take to do the same piece of work? O (A) 12 days O (B) 20 days O (C) 15 days O (D) 24 days​

Answer 1

Answer:

15 days

Step-by-step explanation:

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Answer 2

The correct option regarding the time taken by 12 men and 18 women to do the same piece of work is (C) 15 days.

Given:

10 men or 15 women can do a piece of work in 36 days.

To Find:

The days will be 12 men and 18 women take to do the same piece of work.

Solution:

To find the days will be 12 men and 18 women take to do the same piece of work, we will follow the following steps:

Let the efficiency of 1 man = M

Let the efficiency of 1 woman = W

Now,

The efficiency of 10 men = 10M

The efficiency of 18 women = 18W

As we know,

Total work = Efficiency × time of work

As total work is the same so,

Work done by men = work done by women

$10M \times 36 =15W \times 36$

$\frac{M}{W} = \frac{15}{10} = \frac{3}{2}$

So, the efficiency of men is 3 units and women are 2 units.

Now,

Total work =

$10 \times 3 \times 36 = 1080$

Now,

Let the days taken to do the same amount of work = x days.

Work done by 12 men and 18 women =

$12M \times x + 18W \times x = 1080$

$(12 \times 3 \times x ) + (18 \times \: 2 \times x) = 1080$

$36x + 36x = 108$

$72x = 1080$

$x = \frac{1080}{72} = 15 \: days$

Henceforth, The correct option regarding the time taken by 12 men and 18 women to do the same piece of work is (C) 15 days.

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