Find-all-two-digit-numbers-such-that-when-the-number-is-divided-by-the-sum-of-its-digits-the-quotient-is-4-and-the-remainder-is-3-

Question Number 217244 by ArshadS last updated on 07/Mar/25

Find all two - digit numbers such that

when the number is divided by

the sum of its digits the quotient

is 4 and the remainder is 3 .

Answered by Frix last updated on 07/Mar/25

\frac{10 a + b}{a + b} = 4 + \frac{3}{a + b} \land a + b > 3

\Rightarrow

b = 2 a - 1 \land a + b > 3

a = 2 \land b = 3

a = 3 \land b = 5

a = 4 \land b = 7

a = 5 \land b = 9

S = {23, 35, 47, 59}

Commented by ArshadS last updated on 10/Mar/25

Grateful sir!

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