Question

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. Find the time taken by 1 woman as well as 1 man to finish the work if each of them works alone.
A. Time taken by 1 women alone to finish the work: 24 days, and also that taken by 1 man alone: 32 days
B. Time taken by 1 women alone to finish the work: 18 days, and also that taken by 1 man alone: 36 days
C. Time taken by 1 women alone to finish the work: 14 days, and also that taken by 1 man alone: 30 days
D. Time taken by 1 women alone to finish the work: 12 days, and also that taken by 1 man alone: 28 days

Answer 1

Hint: In these types of work done by 1 woman in 1 day = 1/x and work done by 1 man in 1 day = 1/y and remember to use the given information to make equations and use them to find the value of x and y and solve the question.

Complete step-by-step answer:
Let time taken by 1 women to finish the work = x days
Work finished by 1 women in 1 day = 1/x
Similarly, let time taken by 1 man to finish the work = y days
Work finished by 1 man in 1 day = 1/y
Given that 2 women and 5 men complete the work in 4 days
Therefore work finished by 2 women and 5 men in 1 day =1/4
2$ \times $(work finished by 1 women in 1 day) + 5$ \times $(work finished by 1 man in 1 day) = 1/4
2$ \times $1/x+5$ \times $1/y=1/4
2/x+5/y=1/4 (equation 1)
Also, 3 women and 6 men complete the work in 3 days
Therefore work finished by 3 women and 6 men in 1 day = 1/3
3$ \times $(work finished by 1 women in 1 day) + 6$ \times $(work finished by 1 men in 1 day)
3$ \times $1/x + 6$ \times $1/y = 1/3
3/x + 6/y = 1/3 (equation 2)
Our two equation become
From equation 1
 2/x+5/y=1/4 let 1/x = u
And from equation 2
3/x + 6/y = 1/3 let 1/y = v
So, our equation becomes
2u + 5v = 1/4 and 3u+6v = 1/3
Solving 2u + 5v = 1/4
4(2u + 5v) = 1
8u + 20v = 1 (equation 3)
Now solving 3u+6v = 1/3
3(3u + 6v) = 1
9u + 18v = 1 (equation 4)
From equation 3
8u + 20v = 1
u = (1-20v)/8
Putting value of u in equation 4
9u + 18v = 1
9 {(1-20v)/8} + 18v = 1
Multiplying both sides by 8
8$ \times $9 {(1-20v)/8} + 8 $ \times $18v = 8$ \times $1
9(1 – 20v) + 144v = 8
9 – 180v + 144v = 8
v = 1/36
Putting value of v in equation 3
8u + 20v = 1
8u + 20(1/36) = 1
8u + 5/9 = 1
u = 1/18
Hence, u = 1/18, v = 1/36
Nut we have to find x and y
We know that
Since u = 1/x
1/18 = 1/x
Therefore x = 18
We know that v = 1/y
1/36 = 1/y
y= 36
So, x = 18 and y = 36 is the solution of the given equation
Therefore time taken by 1 women to finish the work alone = x = 18 days and time taken by 1 men to finish the work alone in 1 day = y = 36 days.
Hence option B is correct.

Note: In these types of questions let the work finished by 1 women in 1 day = 1/x and work finished by 1 men in 1 day = 1/y then with the help of given information make equations for finding the value of x and y after making the equation let 1/x = u and 1/y = v then put in the equations and find the value of either u or v and use the value to find the other then use the value of u and v to find the value of x and y.