Question : Work done by $(x + 4)$ men in $(x + 5)$ days is equal to the work done by $(x - 5)$ men in $(x + 20)$ days. Then the value of $x$ is:
Option 1: 20
Option 2: 25
Option 3: 30
Option 4: 15
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Correct Answer: 20
Solution :
Given: Work done by $(x + 4)$ men in $(x + 5)$ days is equal to the work done by $(x - 5)$ men in $(x + 20)$ days.
We know,
Total work = number of men × number of days
According to the question,
$(x + 4)(x + 5)=(x - 5)(x + 20)$
⇒ $x^2+9x+20=x^2+15x-100$
⇒ $6x=120$
$\therefore x=20$
Hence, the correct answer is 20.
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