Question

A job was wrongly estimated to be completed in 10 days by x machines. By deploying 3 extra machines, the job was completed in 12 days. If only one additional machine was used, the no. Of days more than that estimated it has taken to complete the job will be :

Answer 1

$\sf\textsf{Answer:-}$

$\sf\textsf{(2x+36)/(x+1) days.}$

$\sf\textsf{Explanation:-}$

$\sf\textsf{This question is based on the concept of algebra and linear equations in one variable.}$

$\sf\textsf{Here's how to to do it.}$

$\sf\textsf{ATQ, (According to the question):-}$

$\sf\textsf{(x+3) machines can do the work in 12 days.}$

$\sf\textsf{so, in 1 day, 1 machine can do, 1/12(x+3) work}$

$\sf\textsf{in 1 day, (x+1) machines can do (x+1)/(12x+36) work.}$

$\sf\textsf{So, (x+1) machines can complete the work in (12x+36)/(x+1) days.}$

$\sf\textsf{Wrong estimate/estimation:-}$

$\sf\textsf{x machine can do 1 work in 10 days.}$

$\sf\textsf{1 machine can do the work in (10x) days.}$

$\sf\textsf{(x+1) machines can do work in (10x/(x+1)) days.}$

$\sf\textsf{So,more time taken = 12x+36/(x+1) - 10x/(x+1)}$

$\sf\textsf{=12x+36-10x/(x+1)}$

 $\sf\textsf{(=2x+36)/(x+1) days}$

$\sf\textsf{So, the time taken is/would be (2x+36)/(x+1) days.}$