Question: When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water. If 7 1/2 gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?

1. 4
2. 8
3. 12
4. 150
5. 225

Correct Answer: A

Solution and Explanation:
Approach Solution 1:
Since the vat is 3 feet deep and water is filled to 2/3 of its capacity, the water is ⅔ x 3 = 2 feet deep. In cubic feet, the water is 60/7.5 = 8 cubic feet in volume. Since the water is 2 feet deep, the base of the vat must be 8/2 = 4 square feet.

Approach Solution 2:
volume = area of base *height
let the area be A
then volume = A*3
now this is filled to 2/3 of its capacity
so volume of water = 2/3*(A*3)
now the volume of water = 60(15/2)= 8 cubic feet
so 2/3*(A*3)= 8
So A = 8/2 = 4

Approach Solution 3:
Let's say total capacity of the vat= x
2x/3= 60 gallon
x= 90 gallon (total capacity)
If 15/2g of water occupies 1 cubic foot of space
then, 90g of water will occupy= 90*2/15 = 12 cubic foot of space in the vat (Total volume)

We can also write:
a*b*c= 12 cubic foot (c=depth; C=3 feet)
a*b*3= 12
a*b= 4 (which is length * breath= area of the base)

“When a rectangular vat that is 3 feet deep is filled to 2/3 of its”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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