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Q.


2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. The time taken by 1 woman alone to finish the work, and also that taken by 1 man alone is:

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a

36 days, 18 days

b

30 days, 18 days

c

40 days, 30 days

d

26 days, 17 days  

answer is A.

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Detailed Solution

Given 2 women and 5 men can together finish work in 4 days, while 3 women and 6 men can finish it in 3 days.
Days taken by women = x
Days taken by men = y
According to the question,
4 2 x + 5 y =1  
2 x + 5 y = 1 4       -----1
Also,
3 3 x + 6 y =1    3 x + 6 y = 1 3      ----- 2
Let 1 x =w and  1 y =m  
Modified equations are,
2w+5m= 1 4       ---- 3
And,
3w+6m= 1 3  
w+2m= 1 9       ----- 4
Multiplying by 2 on both sides,
2w+4m= 2 9  
Subtracting equation 4 from 3,
(2w + 5m) – (2w + 4m) = 1 4 − 2 9   m= 1 4 − 2 9   m= 9−8 36 = 1 36 .  
Now from equation,
2w+4m= 2 9 2w+4 1 36 = 2 9 2w= 2 9 − 1 9 2w= 1 9 w= 1 18  
Now, the values of x and y are,
m= 1 x = 1 36  
x = 36
w= 1 y = 1 18  
y = 18
The time taken by 1 woman alone to finish the work is 36 days.
Time taken by 1 man alone to finish the work is 18 days.
Hence, option 1 is correct.
 
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