Question

15 men can do a piece of work in 80 days. How long will it take to complete the work of 5 men are reduced?​

Answer 1

Question -:

15 men can do a piece of work in 80 days. How long will it take to complete the work if 5 men are reduced?

Explanation -:

In this question we are provided that 15 men can do a work in 80 days and we are asked to calculate the time if 5 men are reduced that means we need to calculate the no. of days 10 men will take to do the same work.

There are two methods to solve this question

• Unitary Method
• Method of proportion

`\small \red{ \underline{\bf{ Unitary \: Method }}}`

15 men can do a piece of work in 80 days

1 men can do a piece of work in 80 × 15 days

10 men can do a piece of work in
`(80 × 15)/(10)` = 120 days

• Hence, 15 men can do a piece of work in 80 days. It will 120 days to complete the work if 5 men are reduced.

`\rule{40mm}{5pt}`

`\small \orange{ \underline{\bf{ Method \: of \: proportion}}}`

Let us assume that 10 men can do a piece of work in x days.

`\begin{array}{cc} \bf{Number \: of \: men} & \bf {Number \: of \: days} \\ 15&80 \\ 10&x\end{array}`

`\small\bf{ 15 : 10 :: x : 80}`

`➲ \: \small\rm{10 * x = 80 * 15}`

`➲ \: \small\rm {x = (80 * 15)/(10) = 120 \: days }`

x = 120

• Hence, 15 men can do a piece of work in 80 days. It will 120 days to complete the work if 5 men are reduced.

`\rule{72mm}{6pt}`

Answer 2

120 days

Explanation:

Remark

It's an inverse relationship. As the number of men go up, the 80 gets smaller. As the number of men goes down, the number of days will get larger.

Equation

80 = k / 15 Multiply both sides by 15

Solution

80*15 = 15 * k/15

1200 = k

That means that k is number that 80 men will produce. It is the number that relates men and days.

So now you want to put 10 men where 15 were before and see what that does to the number of days.

days = 1200/10

days = 120

Answer

It will now take 120 days.