What is the missing Ramanujan number for the following: $10^{3} + 27^{3} = 19^{3} +__^{3}$ ?

12

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24

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36

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48

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Solution

The correct option is B $24$
Ramanujan number is expressible as the sum of two cubes in two different ways.
So,
$10^{3} + 27^{3} = 19^{3} + ?$
$10^{3} + 27^{3} = 19^{3} + 24^{3}$
$1000 + 19683 = 6859 + 13824$
$20683 = 20683$
So, the missing number is $24.$

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