Question

Find a two digit number such that four times the sum of its digits and three times
the product of its digits are both equal to that number.​

Answer 1

Step-by-step explanation:

let unit place digit be x and tenth place digt y.

then the number is 10y + x

number equals 4 times of sum of digits,

=> 10y + x = 4(x + y).............eq.1

=> 10y + x = 4x + 4y

=> 10y - 4y = 4x - x

=> 6y = 3x

=> x = 6/3 y

=> x = 2y

number equal 3times product of its digits,

=> 10y + x = 3 (xy)..................eq.2

by substituting for x from eq.1 , eq.2 is writen as

4( x + y ) = 4 ( 2y + y )

= 4 × 3y

= 12y

3 (xy) = 3 (2y × y)

= 3 × 2ysquare

= 6y square

6y square = 12y

=> y square/ y = 12/6

=> y = 2

=> x = 2y

=> x = 2 × 2

=> x = 4

the number is

10y + x = 10×2 + 4

= 20 + 4

= 24

ans: 24