Question

A two digit number is four times the sum and three time the product of its digits. Find the numbers.

Answer 1

Let the digits at tens and units place of the number be x and y.

Number = 10× x + y = 10x +y

Given: Number = 4 × sum of digits
10x + y = 4(x+y)
10x + y = 4x +4y
10x -4x  = 4y -y
6x = 3y
y = 6x/3= 2x
y = 2x………………(1)

Number = 3 × product  of digits.( GIVEN)
10x + y = 3(xy)
10x +y = 3xy
10x + 2x = 3x(2x)   [from equation 1]
12x = 6x²
6x² -12x = 0
6x(x -2) = 0
6x = 0 or x - 2=0

x= 0 or x= 2

Tens digit cannot be zero(given number is a two digit number). So x = 2
Put the value of x= 2 in equation 1,

y  = 2x = 2×2= 4
y = 4

Required number = 10x +y
= 10 × 2 +4 = 20 +4
= 24

Hence, the required number is 24.

HOPE THIS WILL HELP YOU..

Answer 2

Let the unit digit be x
and tens digit be y


Required number :- 10y + x

• Number is 4 times the sum of digit

10y + x = 4 ( x + y )

10y + x = 4x + 4y

10y - 4y = 4x - x

6y = 3x

( dividing both side by 3 )

2y = x .... ( i )

• Number is three times the product of its digit.


10y + x = 3xy ... ( ii )

Putting value of x from ( i ) in ( ii )

10y + 2y = 3 × 2y × y

12y = 6y²

6y² - 12y = 0

6y ( y - 2 ) = 0



• 6y = 0

y = 0

( y is tens digit and it can't be 0 so it is neglected )


• ( y - 2 ) = 0

y = 2

Putting value of y in ( i )

2y = x

x = 4

Required number :- 10y + x

10 × 2 + 4

20 + 4

24

Required number is 24