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Urgent mathematical problems
1. solution:

The cooperation between Party A and Party B takes 48 days to complete, so the cooperation efficiency of Party A and Party B is1/48;

Party A works alone for 63 days, and then Party B works alone for 28 days, which is equivalent to 28 days of cooperation between Party A and Party B, and then Party A works alone for 63-28=35 days. After 28 days of cooperation, 28*( 1/48)=7/ 12, leaving 1-7/ 12. The work efficiency of Party A is (5/ 12)/35= 1/84, so the work efficiency of Party B is1/48-1/84 =1/kloc-0.

Now if A works alone for 42 days, then 42* 1/84= 1/2 can complete the task.

The remaining 1- 1/2= 1/2 is completed by Party B alone, so it takes (1/2)/(112) = 56 days.

Or column like this:

Let the total amount be z, where A does X every day and B does Y every day.

63x+28y=48(x+y)

3x=4y

A It takes 84 days for one person to finish it.

(z-42x)/y=(84x-42x)/(3x/4)=56

It will take another 56 days.

2. The lights numbered 1, 2, 4, 6 and 7 are on.

Think about solving problems:

* * * There are 8 lights, and one * * * is pulled 500 times.

500÷8=62 ... four

Pull each lamp at least 62 times. Since 62 is an even number, the state of the lamp remains unchanged.

The remaining four times, lights 1, 2, 3, 4 are pulled, lights 1, 2, 4 are on, lights 3 are off, lights 1, 2, 4, 6, 7 are on. (Exactly, don't believe it /ZL/56/)

3. After the first pour of 1L, it is 9/ 10=90%.

The second pouring is 1*90%=0.9 liter, which means 9-0.9=8. 1, which means 8 1%.

The third pouring1* 81%= 0.81,the remaining alcohol was 8. 1-0.8 1=7.29, and the concentration was 72.9%.