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Find the number which when divided by 61 gives 27 as quotient and 32 as remainder.

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1759

1679

1543

1249

answer is B.

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Detailed Solution

Given that when 61 is divided by a number it gives 27 as quotient and 32 as remainder.
As per the Euclid’s Division algorithm, for any two positive integers say ‘a’ and ‘b’, two unique whole numbers say ‘q’ and ‘r’ exist such that

a = b q + r

where

0 ≤ r ≤ b

.
So, assume the number to be a.
Then by Euclid’s Division algorithm, we have,

a = b q + r

………. (i)
Now, as per the given condition, we have b = 61, q = 27 and r = 32.
Substituting these in equation (i) and simplifying, we get

a = 61 × 27 + 32 a = 1647 + 32 a = 1679

So, the required number is obtained as 1679.
Hence, the correct option is (2).

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