Question

15 men or 24 women or 36 boys can do a piece of work in 12 days working 8 hours a day . how many man must be associated with 12 women and 6 boys to do another piece of work 9/4 times as great in 30 days working 6 hours a day

Answer 1

If 15 men or 24 women or 35 boys do a piece of work in 12 days working 8 hrs a day, how many men must be associated with 12 women and 6 boys to do another piece 9/2 times as great in 30 days working 6 hrs a day 

(a) 8 men 
(b) 10 men 
(c) 12 men 
(d) 4 men 
(e) 15 men 

First piece of work = 15x12x8 man hours = 24x12x8 woman hours = 35x12x8 child hours 

Second piece of work = 9/2 x 15x12x8 man hours 
= A x 30 x 6 
where A is the number of men, if the group composed of only men. 

A = 36 men 

Lets compute the ratios: 
1 woman = 15/24 man 
1 child = 15/35 man 

So 12 women + 6 boys = 12x15/24 + 6x15/35 = 141/14 = 10.08 

Number of men needed = 36 - 10.08 = 26
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Answer 2

The 8 men are required to complete the piece of work.

Given,

15 men or 24 women, or 36 boys can do a piece of work in 12 days, working 8 hours a day.

12 women and 6 boys to do another piece of work 9/4 times as great in 30 days working 6 hours a day.

To Find,

The number of men.

Solution,

Let's form the equation using the above information,

We can write 9/4 as 2.25.

Let the number of men be 'm'

15m(8×12)=24w(8×12)=36b(8×12)

5m=8w=12b, LCM of (5,8,12)=120

m=24, w=15, b=10

Work = 15m(8×12)=15×24(96)

Now req work is 9/4(15×24×96)=9×15×6×96

Total eff=(m+12(15)+6(10))(30×6)=9×15×6×96

m=432–240=192

m=192/24

On Dividing, we get,

m=8

8 men are required.

The 8 men are required to complete the piece of work.

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