- 12 men can finish a work in 10 days


To find out how many more men are needed to complete the work in six days, we need to calculate the work rate of the 12 men.

- Let's assume that the total work is denoted by "W".
- Since 12 men can complete the work in 10 days, the work rate of the 12 men is given by W/10.


- The total work can be calculated by multiplying the work rate of the 12 men by the number of days it takes them to complete the work.
- So, the total work is equal to (W/10) x 10 = W.


- To calculate the work rate for 6 days, we divide the total work by the number of days.
- So, the work rate for 6 days is given by W/6.


- Let's assume that the number of additional men required is denoted by "x".
- The total work done by the additional men in 6 days is given by (W/6) x 6 = W.
- Since the work rate of each man is W/6, the total work done by x men in 6 days is given by (W/6) x x.


- The total work done by the 12 men and the additional x men should be equal to the total work.
- So, we have the equation (W/10) x 10 + (W/6) x x = W.


- Simplifying the equation, we get 12W/10 + xW/6 = W.
- Multiplying both sides of the equation by 30 to eliminate the denominators, we get 12W x 3 + xW x 5 = 30W.
- Simplifying further, we get 36W + 5xW = 30W.
- Subtracting 30W from both sides, we get 6W + 5xW = 0.


- Combining like terms, we have 11xW = -6W.
- Dividing both sides by -6W, we get 11x = -6.
- Dividing both sides by 11, we get x = -6/11.


- Since the number of men cannot be negative, we cannot complete the work in 6 days by adding more men.
- In fact, we would need to remove some men to complete the work in a shorter time.
- Therefore, we cannot determine the exact number of additional men required to complete the work in six days.