4 men and 3 women can finish a piece of work in 6 days whereas if ther

Question

4 men and 3 women can finish a piece of work in 6 days whereas if there were 5 men and 7 women, they would have taken 4 days to finish the work. How many days will 1 man and 1 woman take to finish the work?

A. 156/5
B. 156/7
C. 156/9
D. 156/11
E. 156/13

A. 156/5
B. 156/7
C. 156/9
D. 156/11
E. 156/13

sujoykrdatta · Answer

Question) 
4 men and 3 women can finish a piece of work in 6 days whereas if there were 5 men and 7 women, they would have taken 4 days to finish the work. How many days will 1 man and 1 woman take to finish the work?

Solution: 
We have been given information about the number of people required to complete the work in 6 days and 4 days. Let us make the number of days equal, say, 1 day.

Number of people required to complete the work in 6 days = 4 men and 3 women
=> Number of people required to complete the work in 1 day = 6*4 men and 6*3 women = 24 men and 18 women

Number of people required to complete the work in 4 days = 5 men and 7 women
=> Number of people required to complete the work in 1 day = 4*5 men and 4*7 women = 20 men and 28 women

Thus, we have:

24 men and 18 women are equivalent to 20 men and 28 women
=> 4 men are equivalent to 10 women
=> 1 man is equivalent to 2.5 women

=> 1 man and 1 woman together is equivalent to 3.5 women
Also, 4 men and 3 women are equivalent to 13 women

Thus, from the given relation, we have: 
13 women take 6 days to complete the work
=> Time taken by 3.5 women = 13*6/3.5 = 156/7 days

Answer B

Alternate approach: 
4 men and 3 women take 6 days to complete the work
We need to determine the time taken by 1 man and 1 woman

Taking 1/4th of 4 men and 3 women, we would need 4 times the time, i.e. 6*4 = 24 days

=> 1 man and 0.75 women would take 24 days
Thus, 1 man and 1 woman would take somewhere around 24 days (slightly less than 24)

Let us use the 2nd statement: 
5 men and 7 women take 4 days to complete the work
We need to determine the time taken by 1 man and 1 woman

Taking 1/5th of 5 men and 7 women, we would need 5 times the time, i.e. 4*5 = 20 days

=> 1 man and 1.4 women would take 20 days
Thus, 1 man and 1 woman would take somewhere around 20 days (slightly more than 20)

=> Only option is B

BhishmaNaidu99 · Answer

let the total work be 24 units 
let m = work done by men in one day , and for women = w

work done by 4 men and 3 women in one day is 24/6 = 4 units , 4m+3w = 4
work done by 5 men and 7 women is one day is 24/4 = 6 units , 5m+7w = 6

solving the equations we get, work done by 1 men in one day m = 10/ 13 and women w = 4/13 
 
Together they do total work = 14/13 units in one day

to complete the work 24 units its takes 24*13/14 = 156/7 days

CrackverbalGMAT · Answer

The objective is to find the work done by 1 man and 1 woman

Equation 1  : 4M + 3W= \frac{1}{6}  (work done in 1 day) or 24M + 18W = 1

Equation 2  : 5M + 7W =  \frac{1}{4}  or 20M + 28W = 1

Equating and solving: 24M + 18W = 20M + 28W

4M = 10W

Therefore 1M =  \frac{10}{4} W =  \frac{5}{2}  - - (Equation 3)

Putting in equation 1  : 4* \frac{5}{2} W + 3W = 13W =  \frac{1}{6}

Therefore 1 Woman's 1 days work =  \frac{1}{78}

Putting in Equation (3)   : 1M =  \frac{5}{2}  =  \frac{5}{2}  *  \frac{1}{78}  =  \frac{2.5}{78}

Work done by 1 man and 1 woman in 1 day =  \frac{5}{156}  +  \frac{1}{78}  =  \frac{5+2}{156}  =  \frac{7}{156}

Therefore Time taken = Inverse of 1 days work =  \frac{156}{7}

Option B

Arun Kumar

Sushil117 · Answer

given 
(4M+3W)6=(5M+7W)4 (same work)
24M+ 18W = 20M + 28 W
4M =10 W
now 1M + 1W= 5/2W+ W= 7/2W
 so 7/2WxT = (4M+3W)6 (T= no of days)
 7/2 WxT= 13Wx6 ( as 4M =10W)
 T= 156/7
answer B

Fisayofalana · Answer

This approach takes me 3-4 minutes.

I basically use the substitution method and find out what M and W are.

4m+3w=1/6 and 5m+7w=1/4

1. I make m the same number for each equation by multiplying the first equation by 5 and the second by 4. This gets me: 20m+15w=5/6 and 20m+28w=1
2. I subtract the smaller equation from the larger and get w=1/78
3. Plug back into any original equation to get m. m=5/156
4. Answer the question: 5/156 + 1/78 =1/x

Answer is B: 156/7

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