2 women and 5 men can together finish an ambroidary work in 4 days. while 3 women and 6 men finish it in 3 days. find the time taken by 1 woman alone to finish the work and also time taken by 1 men alone
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Asked on January 17, 2020 by
Yashi Azmi
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.
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ANSWER
Let the work done by man and woman per day be x and y respectively.
When the work is completed in 4 days
Since 5 men and 2 women complete the work in 4 days
therefore work done by 5 men and 2 women in 1 day =
4
1
∴5x+2y=
4
1
⟶eq
n
1
When the work is completed in 3 days
Since 6 men and 3 women complete the work in 3 days
therefore work done by 6 men and 3 women in 1 day =
3
1
∴6x+3y=
3
1
⟶eq
n
2
Multiplying by 3 in eq
n
1, we get
⇒15x+6y=
4
3
⟶eq
n
3
Multiplying by 2 in eq
n
2, we get
⇒12x+6y=
3
2
⟶eq
n
4
On subtracting eq
n
4 from eq
n
3, we get
⇒15x+6y−12x−6y=
4
3
−
3
2
⇒3x=
12
1
⇒x=
36
1
On substituting the value of x in eq
n
2, we get
⇒6×
36
1
+3y=
3
1
⇒3y=
3
1
−
6
1
⇒y=
18
1
Thus,
work done by 1 man in 1 day =
36
1
days
∴ Time taken by 1 man alone to finish the work =36 days
work done by 1 woman in 1 day =
18
1
days
∴ Time taken by 1 woman alone to finish the work =18 days