Can someone explain how to solve them?

We need to find the time taken by 8 machines to complete the job, working at the same rate as 16 machines. We can do this by ratio-proportion method also. Machines : Time 10 : 16 hrs 8 : x hrs Note: This is the case of inverse variation, as increasing the no. of workers would decrease the time taken. So, 10/8 = x/16, which when solved gives x = 20 hours. [spoiler]The correct answer is (B).[/spoiler]

Here, we have 16 identical machines which work for 10 hours. Multiplying the number of workers by the amount of time tells us how many hours in total of machine-work we need to complete the job. Here, we need 160 hours of machine-work. So to complete the job, we need to have our machines work for a total of 160 hours. With 8 machines, we'll need 160/8 = 20 hours of work from each. The principle here is used all the time in management - we're just using the principle of 'person-hours'. If a manager has a job which requires a total of, say, 12 hours of work, then by assigning one employee to the job, it will get done in 12 hours. By instead assigning 2 employees, the job will be done in 6 hours; or, by assigning 3 employees, the job will be done in 4 hours; etc. Whenever we have machines (or people, etc) which work at *identical* rates, we can use this principle. For the other question, I'd first list the numbers in increasing order: 13, 22, 31, 38, 47, 69, 73, 82 We have eight numbers in total. If a number is greater than 3/4 of these, it must be greater than (3/4)*8 = 6 of these numbers. So it must be greater than the six smallest numbers, and thus greater than 69. If a number is less than 1/4 of these, it must be less than 2 of them, so must be less than the largest two numbers, and thus less than 73. So any answer choice strictly between 69 and 73 would be a good answer here.