A certain piece of work was to be completed by 4 men and 8 women. They complete (2/5th) of the work in 4 days. 3 men joined them and together they completed the remaining work in 2 days less than what the initial team would have taken. If the work was to be completed by 20 men, how many days would they take?
Answers
Answer:
certain piece of work was to be completed by 4 men and 8 women. They complete (2/5th) of the work in 4 days. 3 men joined them and together they completed the remaining work in 2 days less than what the initial team would have taken.
If the work was to be completed by 20 men, then they would have taken 3 days.
Step-by-step explanation:
Step 1:
It is given that,
The amount of work done by 4 men & 8 women in 4 days = th
So, the amount of work done by 4 men & 8 women in 1 day will be = =
th of work
∴ 4 men + 8 women can complete the work in 10 days ....... (i)
and
Also, The remaining work i.e., 3/5th of work is done by 4 men + 8 women in 10 - 4 = 6 days
Step 2:
Now, 3 more men joined the group of (4 men + 8 women) and because of which the remaining work i.e., (1 - 2/5 = 3/5th work) is done in 2 days less than what the initial team would have taken i.e., (6 - 2) = 4 days.
New team becomes = 4 men + 8 women + 3 men = 7 men + 8 women
By using the Man-Days formula, we get
[(4men+8women) * 4] / (2/5) = [(7men+8women) * 4] / (3/5)
⇒ [(4men+8women) * 2] = [(7men+8women) * 4] /3
⇒ [(4men+8women) * 6] = [(7men+8women) * 4]
⇒ 24 men + 48 women = 28 men + 32 women
⇒ 16 women = 4 men
⇒ 1 men = 4 women ........ (ii)
Therefore, from eq. (ii), we can write
4 men + 8 women as ⇒ 4 men + (1/4 * 8) men = 4 men + 2 men = 6 men can complete the work in 10 days ..... [as written in eq. (i)]
Finally, by using the Man-Days formula again, we get
6 men * 10 days = 20 men * (no. of days)
⇒ No. of days = 3 days
Thus, 20 men would have taken 3 days to complete the work.
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