Ratios & Proportion
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Q.

If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days?

 A.

120 men

 B.

122 men

 C.

128 men

 D.

134 men

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Solution:
Option(B) is correct

Let's try solving this Problem using ratio approach.

Amount of work done by 20 men = 24 women = 40 boys or 1 man = 1.2 woman = 2 boys.

Let us, therefore, find out the amount of men required, if only men were working on the job, to complete the new job under the new conditions and then make adjustments for the women and children working with the men.

The man hours required to complete the new job = 4 times the man hours required to complete the old job. (As the new job is 4 times as big as the old job)

Let $n$ be the number of men required.

$n \times 5 \times 12 = 20 \times 8 \times 12 \times 4$= or $n=128$

i.e. 128 men working on the job will be able to complete the given job.

However, the problem states that 6 women and 2 boys are working on the job.

6 women $=\dfrac{6}{1.2}= 5 men and 2 boys = 1 man.

∴ The equivalent of $5+1=6$ men are already working.

Thus, final number of men working,

$=128-6 = \textbf{122 men}$


(6) Comment(s)


Raj Karan
 ()

ratio and direct and indirect relation method

(20*4*8*1)/5=128

six already working so 122 more required

now the multiplying factors here are

(1) work increases in 1:4 so number of men required increases in ratio 4:1

(2) per hour rate of doing work decreases in the ratio 5:8, so number reqd increases in the ratio 8:5

3) total days remain same hence multiplying factor is 1



Maddy
 ()

wrong solution because it's $12*8*2*4=9=(n+6)*12*5$ which implies $n=122$


Nimeesh
 ()

I guess you are making mistakes in writing $n+6$ as it should be $n-6$.

P.S. there are other conceptual mistakes too in your approach.


Rakesh Babu
 ()

I don't understand the logic here

20 men working 8hrs a day can complete the work in 12 days

But only 2men working 5hrs a day with 6women and 2boy can complete the work in 12 days

Less number of hours, more work, same days, less labor(women+boy) but fewer men



Anil Negi
 ()

My calculation has gone wrong.

128 men will be required.

As 6 women = 5 men, 2 boys = 1 man,

6 men are already working.

So the answer is

128-6 = 122 men



Ishita
 ()

As the work becomes 4 times so it should be divided by new work equation i.e.

$xM+5M(=6W)+M(=2B)*12*5/4=20M*12*5$