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The difference in volumes of two cubes is 152 m 3 and the difference in their one face areas is 20 m 2. If the sum of their edge is 10 m, the product of their edge is?

Correct Answer: 24

Explanation:

Let the edges of the two cubes be x and y metres
Then, x3 - y3 = 152
and x2 - y2 = 20
Also, x + y = 10
So, x - y = (x2 - y2) / (x + y) = 20/10 = 2
Now, (x3 - y3) / (x - y) = 152/2
⇒ x2 + y2 + xy = 76
⇒ (x + y)2 - xy = 76
⇒ xy = (x + y)2 - 76 = (10)2 - 76 = 24


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