550 people can complete a work in 100 days. After 10 days, 50 more people joined. In how many more days the work will be completed?

To solve this problem, we can use the concept of man-days.

Given that 550 people can complete the work in 100 days, we can calculate the total man-days required to complete the work. This can be done by multiplying the number of people by the number of days: 550 * 100 = 55,000 man-days.

After 10 days, the work has already been in progress. So, we need to calculate the remaining man-days required to complete the work.

In the first 10 days, 550 people worked, which means they contributed 550 * 10 = 5,500 man-days.

Now, 50 more people joined, making the total number of people working on the project 550 + 50 = 600.

To find out how many more days it will take to complete the work, we need to calculate the remaining man-days and divide it by the number of people working.

The remaining man-days can be calculated by subtracting the man-days already contributed from the total man-days required: 55,000 - 5,500 = 49,500 man-days.

To find out how many more days it will take to complete the work, we divide the remaining man-days by the number of people working: 49,500 / 600 = 82.5 days.

Since we cannot have half a day, we round up to the nearest whole number. Therefore, it will take approximately 83 more days to complete the work with the additional 50 people.

So, in total, the work will be completed in 10 + 83 = 93 days.