Question

a work is assigned to 6 men and 12 women and they could complete it in 3 days.it was also observed that together they can do 7 times as much work a man and a woman can do. in how many days would 14 have done the work

Answer 1

Answer:

9 days is correct answer

Step-by-step explanation:

6m + 12w = 3 days …….(1)

6m + 12w = 7 (m + w)

6m + 12w = 7m + 7w

6m + 12w = 6m + 1m +7w

6m + 5w + 7w = 6m + 1m + 7w

1 man = 5 woman

30w + 12w = 3 days

42w = 3 day

14 women =

= 9 days

Answer 2

Correct Question :- A work is assigned to 6 men and 12 women and they could complete it in 3 days.it was also observed that together they can do 7 times as much work a man and a woman can do. in how many days would 14 women have done the work ?

Solution :-

Let us assume that, the efficiency of a man is M unit/day and efficiency of a woman is W unit / day .

So,

→ 6 men complete work in 1 day = 6 * M = 6M

→ 12 women complete work in 1 day = 12 * W = 12W

then,

→ 6 men + 12 women complete work in 1 day = 6M + 12W

therefore,

→ They complete work in 3 days = Total work = 3(6M + 12W)

also, given that, together they can do 7 times as much work a man and a woman can do.

So, we can say that, they did 7 times of the total work done by 1 man and 1 woman per day .

→ Total work done by 1 man and 1 woman per day is = (1M + 1W)

then,

→ 6M + 12W = 7(1M + 1W)

→ 6M + 12W = 7M + 7W

→ 12W - 7W = 7M - 6M

→ 5W = 1M

therefore, we can conclude that, efficiency of 1 man is equal to efficiency of 5 women .

hence,

→ Total work = 3(6M + 12W) = 3[6(5W) + 12W] = 3[30W + 12W] = 3 * 42W = 126W

now,

→ Efficiency of 14 women per day = 14 * W = 14W .

So,

→ Time taken by them to complete total work = Total work / Efficiency of 14 women = 126W/14W = 9 days (Ans.)

∴ 14 woman would have done the work in 9 days .

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