What is the value of _ for the Ramanujan number: _ $+ 54^{3} = 38^{3} + 48^{3}$ ?

10

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20

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30

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40

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Solution

The correct option is C $20$
Ramanujan number is the number expressible as the sum of two cubes in two different ways.
So,
$20^{3} + 54^{3} = 38^{3} + 48^{3}$
$8000 + 157464 = 54872 + 110592$
$165464 = 165464$
So, the missing number is $20.$

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