Question

A division problem given in school resulted in a quotient of 57 and a remainder of 52. One student who had solved the problem wasn't quite sure of his figuring efficiency and so he made a test by multiplying the quotient with the divisor and adding the remainder. The result was 17,380, which unfortunately was in no way identical with the original dividend. The reason was that the student when doing the multiplication had mistaken a six, the second figure of the divisor from the right, for a zero. What was the original division problem?

Answer 1

Given :- A division problem given in school resulted in a quotient of 57 and a remainder of 52 . One student made a test by multiplying the quotient with the divisor and adding the remainder. The result was 17,380 . The student when doing the multiplication had mistaken a six, the second figure of the divisor from the right, for a zero.

To Find :- What was the original division problem ?

Answer :-

→ Quotient = 57 .

→ Remainder = 52 .

→ Result was = 17380 .

so,

→ Divisor was = (17380 - 52) / 57 = (17328/57) = 304 .

now, given that, The student had mistaken a 6 the second figure of divisor from the right , for a 0 .

then, we can conclude that, Students did mistake in divisor of 364 as 304 .

therefore,

→ The original divison = 364 * 57 + 52 = 20748 + 52 = 20800 (Ans.)

Hence, the original division problem was 20800 .

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