One man can do as much work in one day as a woman can do in 2 days. A

Question

One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all $1113 at the end of the days work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?

(A) $5
(B) $7
(C) $14
(D) $14
(E) $20

Are You Up For the Challenge: 700 Level Questions

(A) $5
(B) $7
(C) $14
(D) $14
(E) $20

Are You Up For the Challenge: 700 Level Questions

yashikaaggarwal · Answer

Let work be 1
A Man do 1 work a day
A woman do 1/2 work a day, and 
A child do 1/6 work a day.
Or the work ratio of M:W:C is 6:3:1 ------(1)

Estate owner hire 39 workers in the ratio of 6:5:2.
Equals to 18M:15W:6C -----(2)

18 men do 6 work a day = 108
15 women do 3 work a day = 45
6 children do 1 work a day = 6
Total is 108+45+6=159
Total wage given/day = 1113/159=7
So 6 children will get 7$ per head.
Answer is B

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RaghavKhanna · Answer

Let,
No. Of men = 6x
No. Of women = 5x
No. Of children = 2x

6x + 5x + 2x = 39
=> x = 3

Now,
1 man = 2 women
And, 1 woman = 3 child
So, 1 man = 6 children

Let child receive amount p.

=> (6 x 3 x 6 x p) + (5 x 3 x 3 x p) + (2 x 3 x p) = 1113
108p + 45p + 6 p = 1113
p = 7

sujoykrdatta · Answer

Comparing efficiencies per day: Efficiency of a man = 2 * Efficiency of a woman
Comparing efficiencies per day: Efficiency of a woman = 3 * Efficiency of a child
Combining: Efficiency of a man = 2 * Efficiency of a woman = 6 * Efficiency of a child

Assuming that a child does 1 unit work per day: Work done by a woman per day = 3 units; Work done by a man per day = 6 units

Ratio of men, women and children = 6 : 5 : 2
=> Work done per day is proportional to 6*6 + 5*3 + 2*1 = 53 units; which is equivalent to $1113
=> Each unit of work is equivalent to 1113/53 = $21
=> Amount obtained by the children who do equivalent to 2 units of work = $21 x 2 = $42

Since there were 39 people, number of children = 2/(6+5+2) x 39 = 6
Thus, $42 was obtained by 6 children

=> Amount obtained by each child = 42/6 = $7

Answer B

lacktutor · Answer

One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all $1113 at the end of the days work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?

(A) $5
(B) $7
(C) $14
(D) $14
(E) $20

Are You Up For the Challenge: 700 Level Questions

Man -  \frac{1}{1} 
Women -  \frac{1}{2} 
Child -  (\frac{1}{3})(\frac{1}{2})= \frac{1}{6}

6x+ 5x+2x= 39 
 13x = 39 
 x = 3 
--> 18 men, 15 women and 6 children are hired.

18(\frac{1}{1})x + 15(\frac{1}{2})x+ 6(\frac{1}{6})x = 1113 
 18x+ (\frac{15}{2})x+ x= 1113 
 \frac{53x}{2} = 1113 
--->  x= 42  
 \frac{42}{6} =7  $ for each child

Answer (B).

AnirudhaS · Answer

Let m=man, w=woman, c=child

1 m --> 1 day --> 1 work
1 w --> 1 day -->  \frac{1}{2}  work
1 c --> 1 day -->  \frac{1}{2}*\frac{1}{3} = \frac{1}{6}  work

Now proportion of people working = m:w:c = 6:5:2 = 18:15:6 (18+15+6=39)
So there are 6 children working, let us keep this in mind

18 m --> 1 day --> 18 work
15 m --> 1 day -->  \frac{15}{2}  work
 6 c --> 1 day --> 1 work

So proportion of work --> man:woman:child = 18: \frac{15}{2} :1 = 36:15:2

Therefore, all children got = $1113 * \frac{2}{53}  = $42
Each child got = $42/6 = $7

Answer:  B

ScottTargetTestPrep · Answer

For the number of men, women, and children, we can create the equation:

6x + 5x + 2x = 39

13x = 39

x = 3

Therefore, there are 6(3) = 18 men, 5(3) = 15 women, and 2(3) = 6 children.

If we let a = the amount paid to each child, then 3a = the amount paid to each woman, and 6a = the amount paid to each man (that is because a man works twice as fast as a woman, who in turn is 3 times as fast as a child). We can create the equation:

18(6a) + 15(3a) + 6(a) = 1113

108a + 45a + 6a = 1113

159a = 1113

a = 7

Answer: B

shwetakoshija · Answer

Question Stem: 
 
 A man does as much work in 1 day as a woman does in 2 days. 
 A child does 1/3 the work of a woman in a day. 
 Total hired workers = 39 (men, women, children in the ratio 6:5:2). 
 Total wages paid = $1113.
 
 Wages are proportional to work done.

To find:  Daily wage of a child.

Solution:

Part 1: Find the number of men, women, and children
 
 Let number of Men = 6x, Women = 5x, Children = 2x.
 
 6x + 5x + 2x = 39 
 13x = 39 => x = 3  
 
 So, no. of Men = 6(3) = 18, Women = 5(3) = 15, Children = 2(3) = 6

Part 2: Find work done by the men, women, and children
 
 Let a woman’s 1 day work = 1 unit.
 
 Then, a man’s 1 day work = 2 units (since 1 man = 2 women in work rate). 
 And a child’s 1 day work = 1/3 unit.  
 
 Total work done in 1 day:
 
 18 Men: 18 × 2 = 36 units 
 15 Women: 15 × 1 = 15 units 
 6 Children: 6 × 1/3 = 2 units 
 Total work done = 36 + 15 + 2 = 53 units

Part 3: Wages 
 
 Total wages = $1113
 
 So, wage per unit work = 1113 ÷ 53 = $21 
 Child’s daily wage (for 1/3 unit per day) = (1/3) × 21 = $7

Correct Answer: (B)

Shweta Koshija  
 GMAT, GRE, SAT Coach for 10+ years

One man can do as much work in one day as a woman can do in 2 days. A

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