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Question

The cube of a number is 8 times the cube of another number. If the sum of the cubes of numbers is 243, what is difference of the numbers ?

A
4
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B
6
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C
-6
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D
3
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Solution

The correct option is D 3
Let the number be x and another number be y then according to question,
x3=8×y3(i)
and the sum of their cubes is 243,
x3+y3=243(ii)

Now, from equation (i) and equation (ii) we get,
8y3+y3=2439y3=243y3=2439=27y=3
Now, for x let's put the values of y in equation (i).
x3=8×33x3=2×2×2×3×3×3x=2×3=6

Now, as required in the question, let's take the difference of the two numbers.
xy=63=3

Hence, option 'a' is correct.

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