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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 1 · Set 3 · Q26
The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.
The sum of the digits of a $\displaystyle 2$-digit number is 14. The number obtained by interchanging its digits exceeds the given number by $\displaystyle 18$ . Find the number.
Marking-scheme solution
Let the required number be \(\displaystyle 10 \mathrm{x}+\mathrm{y}\)
Here \(\displaystyle \mathrm{x}+\mathrm{y}=14\)---- (i)
and \(\displaystyle 10 \mathrm{y}+\mathrm{x}=18+10 \mathrm{x}+\mathrm{y}\)
\[\Rightarrow y-x=2 \text {---- (ii) }
\]
Solving (i) and (ii) to get \(\displaystyle \mathrm{x}=6, \mathrm{y}=8\)
∴ required number is 68.
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