Question 15 Marks
A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
Answer
View full question & answer→Let this two digit number be XY. Then as per the question,
$X Y=18 \ldots . . \text { (i) }$
$X Y-63=Y X .\ldots(ii)$
Let this two digit number be 'Xi. Which means $X =10 x$ (as it comes in tens digit).
Then as per the question, $x x y=1$ s ... $10 x+y-63=10 y+x$
$\Rightarrow 9 x-9 y-63=0$
$\Rightarrow x-y-7=0$
$\Rightarrow$ Puting $x=\frac{18}{ y }$ in above, we get
$\Rightarrow 18- y ^2-7 y =0$
$\Rightarrow y ^2+7 y -18=0$
$\Rightarrow y^2+9 y-2 y-18=0$
$\Rightarrow( y +2)( y -9)=0$
As y can't be negative, hence $y=9$
$\Rightarrow$ Hence $x=\frac{18}{9}=2($ from (i))
$\Rightarrow$ Hence answer is 92
Alternate Answer:
From (i), possible combinations are: 29, 36, 63, 92.
From (ii), it's clear that the number ' $Xi$ is more than 63 as that is the only case when we subtract this number by 63 , we get a positive value.
Hence, the number is 92 and when we delete it by 63 , we get a number of 29 which is a numbers where the digits are interchanged.
Hence answer is 92.
$X Y=18 \ldots . . \text { (i) }$
$X Y-63=Y X .\ldots(ii)$
Let this two digit number be 'Xi. Which means $X =10 x$ (as it comes in tens digit).
Then as per the question, $x x y=1$ s ... $10 x+y-63=10 y+x$
$\Rightarrow 9 x-9 y-63=0$
$\Rightarrow x-y-7=0$
$\Rightarrow$ Puting $x=\frac{18}{ y }$ in above, we get
$\Rightarrow 18- y ^2-7 y =0$
$\Rightarrow y ^2+7 y -18=0$
$\Rightarrow y^2+9 y-2 y-18=0$
$\Rightarrow( y +2)( y -9)=0$
As y can't be negative, hence $y=9$
$\Rightarrow$ Hence $x=\frac{18}{9}=2($ from (i))
$\Rightarrow$ Hence answer is 92
Alternate Answer:
From (i), possible combinations are: 29, 36, 63, 92.
From (ii), it's clear that the number ' $Xi$ is more than 63 as that is the only case when we subtract this number by 63 , we get a positive value.
Hence, the number is 92 and when we delete it by 63 , we get a number of 29 which is a numbers where the digits are interchanged.
Hence answer is 92.