Question

A number consists of two digits. The product of the digits is 20. When 9 is added to
the number, the digits interchange their places. Find the number.
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Answer 1

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