Question

A two digit number contains the smaller of two digits in the units place.The product of the digits is 24 and the difference between the digits is 5. Find the number

Answer 1

the required no. is 83

Answer 2

Let the unit digit be x....( Smallest number )
and ten's digit be y.........( Largest number )

Original number :- 10y+x

Now,.
according to question,

xy = 24 ..........( i )

and

y-x = 5

y = 5+x........ ( ii )

Putting the value of y in equation ( i )

xy = 24

x ( 5+x ) = 24

5x + x² = 24

x² + 5x -24 = 0

x² + 8x -3x - 24 = 0

x ( x +8 ) -3 (x +8) = 0

( x-3 ) ( x +8) = 0

( x - 3 ) = 0
x = 3

( x +8 ) = 0
x = -8
( -8 will be neglected )


If x = 3

y = x+5
y = 3+5
y = 8

The required number is :-

10y + x

=> 10×8+3

=>80+3

=>83

@Altaf