The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 7:8 then what is the number of visitors on the 5th day of the library?

Let's solve this step by step:

Step 1: The average number of visitors for the first 4 days is 58. So, the total number of visitors for these 4 days is 58 * 4 = 232.

Step 2: The average number of visitors for the 2nd, 3rd, 4th, and 5th days is 60. So, the total number of visitors for these 4 days is 60 * 4 = 240.

Step 3: To find the number of visitors on the 5th day, we subtract the total number of visitors for the first 4 days from the total number of visitors for the 2nd, 3rd, 4th, and 5th days. So, the number of visitors on the 5th day is 240 - 232 = 8.

Step 4: We know that the number of visitors on the 1st and 5th days were in the ratio 7:8. So, let's say the number of visitors on the 1st day is 7x and on the 5th day is 8x.

Step 5: We know from step 3 that the number of visitors on the 5th day is 8. So, we can set up the equation 8x = 8. Solving for x gives us x = 1.

Step 6: Substituting x = 1 into the equation for the number of visitors on the 5th day (8x) gives us 8 * 1 = 8.

So, the number of visitors on the 5th day of the library is 8.