CAT 1991 — QA Question 31
Answer the following questions based on the information given below:
There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.
A square piece of cardboard of sides ten inches is taken and four equal squares pieces are removed at the corners, such that the side of this square piece is also an integer value. The sides are then turned up to form an open box. Then the maximum volume such a box can have is
Answer & solution
72 cubic inches.
- B
24.074 cubic inches.
- C
2000/27 cubic inches.
- D
64 cubic inches.
If x = 1, then for the rectangular box : l = 8, b = 8 and h = 1, so volume = 64.
If x = 2, l = 6, b = 6 and h = 2 and volume = 72.
If x = 3, l = 4, b = 4 and h = 3 and volume = 48.
Therefore, we can see that for a value of x between 2 and 3, the volume of box decreases and will go on decreasing further as x increases.
Hence, the maximum volume that the box can have is 72 cubic inches.
Hence, option (a).