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 women alone to finish the work, also that taken by 1 man alone.
Answers
Let us assume that, the time taken by woman to complete the work be x days and by man be y days.
2 women and 5 men can together finish an embroidery work in 4 days.
According to question,
⇒ 2/x + 5/y = 1/4
⇒ (2y + 5x)/xy = 1/4
⇒ 4(2y + 5x) = xy
⇒ 8y + 20x = xy...........(1)
On the other hand, 3 women and 6 men can finish it in 3 days.
According to question,
⇒ 3/x + 6/y = 1/3
⇒ (3y + 6x)/xy = 1/3
⇒ 3(3y + 6x) = xy
⇒ 9y + 18x = xy............(2)
On multiplying (eq 1) with 9 and (eq 2) with 8 we get,
⇒ 72y = 9xy - 180x...........(3)
⇒ 72y = 8xy - 144x...........(4)
On comparing we get,
⇒ 9xy - 180x = 8xy - 144x
⇒ 9xy - 8xy = - 144x + 180x
⇒ xy = 36x
⇒ y = 36 days
Substitute value of y in (eq 1)
⇒ 8(36) + 20x = 36x
⇒ 288 = 36x - 20x
⇒ 288 = 16x
⇒ x = 18 days
Therefore,
Woman alone can finish the work in 18 days and man alone in 36 days.
||✪✪ GIVEN ✪✪||
- 2W + 5M can Together Finish a work in = 4 days.
- 3W + 6M can Together Finish a work in = 3 days.
✯✯ To Find ✯✯
- Time Taken by 1 woman Alone ?
- Time Taken by 1 man Alone ?
|| ✰✰ ANSWER ✰✰ ||
Given That, 2 women and 5 men can together finish an embroidery work in 4 days .
So,
➻ Total work = 4(2W + 5M) .
Similarly, 3W + 6M can Together Finish a work in = 3 days.
So,
➺ Total work = 3(3W + 6M)
___________________
Now, Since Work is Same in Both Case ,
So,
⟼ 4(2W + 5M) = 3(3W + 6M)
⟼ 8W + 20M = 9W + 18M
⟼ 20M - 18M = 9W - 8W
⟼ 2M = 1W
⟼ (M/W) = (1/2).
______________
So, we Can say That :-
⟿ Efficiency of 1 Man = 1 unit /day.
⟿ Efficiency of 1 woman = 2 unit/day.
______________
∴ Total work :-
➳ 4(2w + 5M)
➳ 4(2*2 + 5*1)
➳ 4(4 + 5)
➳ 4 * 9
➳ 36 units.
______________
Now,
☛ Time Taken by 1 woman Alone to Complete Total work = (36/2) = 18 days.
☛ Time Taken by 1 man Alone to Complete Total work = (36/1) = 36 days.