A group of men decided to complete a task in 10 days, but five of them remained absent. If the rest of the group completed the task in 12 days, find the original number of men in the group.

Correct option is A

Given:

A group of men initially decides to complete a task in 10 days.

5 men remain absent, so the remaining men complete the task in 12 days. 

Formula Used: 

​$$M_1 \times T_1 = M_2 \times T_2$$ 

Where, $$M_1 , M_2$$ are men and $$T_1 , T_2$$ are time.​

Solution:

Let the original number of men in the group be denoted by x.

Since the amount of work required to complete the task is the same in both cases,

So,

$$x × 10 = (x−5) × 12$$​​

​$$10x=12(x−5)$$

$$10x=12x−60$$ 

$$12x-10x=60$$ 

​​$$2x=60$$

$$x = \frac{60}{2} = 30$$ 

Thus, the original number of men in the group was 30.

​