The sum of a two-digit number and the number obtained by interchanging its digits is 99. The digit in the ten's place is greater than the digit in the unit's place by 3. Find the number.

Q.3 (B)(i) The sum of a two-digit number and the number obtained by interchanging its digits is 99. The digit in the ten's place is greater than the digit in the unit's place by 3. Find the number.

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc 10th Save WhatsApp Report

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Answer: The number is 63.

Let the ten's digit be \(x\) and the unit's digit be \(y\). The number is \(10x + y\) and the reversed number is \(10y + x\).

\((10x + y) + (10y + x) = 99 \Rightarrow 11x + 11y = 99 \Rightarrow x + y = 9\) ...(I)

\(x - y = 3\) ...(II)

Adding (I) and (II): \(2x = 12\), so \(x = 6\); then \(y = 9 - 6 = 3\).

Number \(= 10(6) + 3 = 63\). Check: \(63 + 36 = 99\) and \(6 - 3 = 3\).

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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The sum of a two-digit number and the number obtained by interchanging its digits is 99. The digit in the ten's place is greater than the digit in the unit's place by 3. Find the number.

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