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 lave done the work?

Answer 1

Answer:-

9 days

step-by-step explation:-

6m+12w=3days...(i)

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

6m+12w=7m+7w

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

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

1man=5 woman

30w+12w=3days

42w=3day

14women=

=9days

I hope it's helpful

Answer 2

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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