If a number is divided by $45$ , then the remainder is $32$ . If the same number is divided by $15$ , then the remainder is

2

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3

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16

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4

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Solution

The correct option is C $2$

Let the number is $x$
$\frac{x}{45} = q + 32 q \to q u o t i e n t x = 45 q + 32 = 45 q + 30 + 2 = 15 (3 q + 2) + 2 \frac{x}{15} (3 q + 2) + (2) = k + 2 ∴ r e m a i n d e r = 2$

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