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:

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

36 days, 18 days

30 days, 18 days

40 days, 30 days

26 days, 17 days

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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 = 14

-----1
Also,

3 3 x + 6 y = 1

3 x + 6 y = 13

----- 2
Let

1 x = w and 1 y = m

Modified equations are,

2 w + 5 m = 14

---- 3
And,

3 w + 6 m = 13

w + 2 m = 19

----- 4
Multiplying by 2 on both sides,

2 w + 4 m = 29

Subtracting equation 4 from 3,
(2w + 5m) – (2w + 4m) =

14 − 29

m = 14 − 29

m = 9 − 8 36 = 136 .

Now from equation,

2 w + 4 m = 29 2 w + 4136 = 29 2 w = 29 − 19 2 w = 19 w = 118

Now, the values of x and y are,

m = 1 x = 136

x = 36

w = 1 y = 118

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.

Watch 3-min video & get full concept clarity