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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 2 · Set 1 · Q12
A $\displaystyle 2$-digit number is such that the product of its digits is 24. If $\displaystyle 18$ is subtracted from the number, the digits interchange their places. Find the number.The difference of the squares of two numbers is 180. The square of the smaller number is $\displaystyle 8$ times the greater number. Find the two numbers.
A $\displaystyle 2$-digit number is such that the product of its digits is 24. If $\displaystyle 18$ is subtracted from the number, the digits interchange their places. Find the number.
The difference of the squares of two numbers is 180. The square of the smaller number is $\displaystyle 8$ times the greater number. Find the two numbers.
Marking-scheme solution
Let the two numbers be \(\displaystyle x\) and \(\displaystyle y, \mathrm{x}>\mathrm{y}\)
\[\begin{aligned}
\therefore & x^{2}-y^{2}=180 \\
& y^{2}=8 x
\end{aligned}
\]
Thus \(\displaystyle x^{2}-8 x-180=0\)
\[\Rightarrow(x-18)(x+10)=0
\]
Therefore, \(\displaystyle x=18\)
\[\left.\begin{array}{r}
\text { re, } x=18 \\
y= \pm 12
\end{array}\right\}
\]
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