Doubt by CBSE
Solution :
Solution by using single variable (x) only
Let the digit at the one's place be x
and the digit at the ten's place by 24/x
Therefore
Original Number = (24/x)10+x
Reverse Number = 10x+(24/x)
ATQ
9(x²+2x-24)=0
x²+2x-24=0/9
x²+2x-24=0
x²+(6-4)x-24=0
x²+6x-4x-24=0
x(x+6)-4(x+6)=0
(x+6)(x-4)=0
(x+6)=0 & (x-4)=0
x=-6 & x=+4
x²+6x-4x-24=0
x(x+6)-4(x+6)=0
(x+6)(x-4)=0
(x+6)=0 & (x-4)=0
x=-6 & x=+4
A digit can't be -ve.
Hence x=-6 is rejected.
Hence, x=4
Required Original Number = (24/x)10+x
=240/(4)+4
= 60+4
= 64
Therefore the required two digit number is 64.
Solution by using two variable (x & y) only
Let the digit at the one's place be x
and the digit at the ten's place by y
Therefore
Original Number = 10y+x
Reverse Number = 10x+y
ATQ
xy = 24
y=24/x — (1)
Also
y=24/x — (1)
Also
10y+x - 18 = 10x+y
putting the value of y from equation (1)
9(x²+2x-24)=0
x²+2x-24=0/9
x²+2x-24=0
x²+(6-4)x-24=0
x²+6x-4x-24=0
x(x+6)-4(x+6)=0
(x+6)(x-4)=0
(x+6)=0 & (x-4)=0
x=-6 & x=+4
x²+6x-4x-24=0
x(x+6)-4(x+6)=0
(x+6)(x-4)=0
(x+6)=0 & (x-4)=0
x=-6 & x=+4
A digit can't be -ve.
Hence x=-6 is rejected.
Hence, x=4
putting in equation (1)
y = 24/4
y = 6
y = 6
Required Original Number = 10y+x
=10(6)+4
= 60+4
= 64
Therefore the required two digit number is 64.