Question on work done by `x` machines in some days?

Given that the initial estimated count of machines be `x`
Given that the adjusted count of machines is `x+3`
Given that the new count of days to complete the task is 12 days.

Let the amount of work be measured in 'machine days'.

`color(blue)("Initial condition")`

So the amount of work to complete the work is:

`12(x+3)` machine days.

Set `12(x+3)" machine days "=` the amount of work for 1 job

`12(x+3)=1" "..........................Equation(1)`

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`color(blue)("Changed condition")`

Not 3 but only 1 additional machine is used.

The total amount of work still needs to be done to complete the task.

Let the new count of days be `d`

`d(x+1)=1" "...............................Equation(2)`

Using `Equation(1)` substitute for 1 in `Equation(2)`

`d(x+1)=12(x+3)" ".............................Equation(2_a)`

Divide both sides by `(x+1)`

`d=(12(x+3))/(x+1)`
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`color(blue)("Determine the number of days more than originally estimated")`

`d-10 " "=" "(12(x+3))/(x+1) -10`

Set the value of `1-=(x+1)/(x+1)" "`so `" "10 -=(10(x+1))/(x+1)`

Thus we have:

`d-10 " "=" "(12(x+3))/(x+1) -10`

`" "=" "(12(x+3))/(x+1)-(10(x+1))/(x+1)`

`" "=" "(12x+36-10x-10)/(x+1)`

`" "=" "(2x+26)/(x+1)`

This matches option C