A number consists of two digits. The product of the digits is 20. When

1.	A number consists of two digits. The product of the digits is 20. When 9 is added tothe number, the digits interchange their places. Find the number.
Answer» Step-by-step explanation: let the two digit no. be =10x + y and it's 10 place digit = x and unit place digit = y xy =20............(1) (10x+y) + 9 = 10Y+ x............(2) 10x - x -10y + y +9 =0 9x - 9y + 9 =0 taking 9 common x-y +1=0 using y=x +1 , put in eq 1 x × (x+1)=20 x^2+x - 20=0 ${x}^{2} + 5x - 4x - 20 = 0$ x(x+5) - 4(x +5)=0 (x-4) (x+5)=0 x=4 , x can't be equal to-5 as in a number DIGITS can't be negative y=x+1 y = 4+1 =5 no. =10x +y= 10×5+4=50+4 =54

A number consists of two digits. The product of the digits is 20. When 9 is added tothe number, the digits interchange their places. Find the number.

Answer»

Step-by-step explanation:

let the two digit no. be =10x + y

and it's 10 place digit = x and unit place digit = y

xy =20............(1)

(10x+y) + 9 = 10Y+ x............(2)

10x - x -10y + y +9 =0

9x - 9y + 9 =0

taking 9 common

x-y +1=0

using y=x +1 , put in eq 1

x × (x+1)=20

x^2+x - 20=0

${x}^{2} + 5x - 4x - 20 = 0$

x(x+5) - 4(x +5)=0

(x-4) (x+5)=0

x=4 , x can't be equal to-5 as in a number DIGITS can't be negative

y=x+1

y = 4+1 =5

no. =10x +y= 10×5+4=50+4 =54