Question

A number consisting of two digit is equal to 7 times the sum of its digits when 27 is subtracted from the number the digits interchange their place. Find the no.

Answer 1

Answer:

the no. is 63

Step-by-step explanation:

let the digit at one's place be x .

Value of x=1×x=x

let other digit be y

value of y=10×y=10y

the no. is 10y+x

according to question:

                 10y+x=7(x+y)

and,

                 10y+x-27=10x+y

⇒10y-y-27=10x-x

⇒9y-27=9x

⇒y-3=x

replace value of x in the first equation i.e. 10y+x=7(x+y) as x=y-3

⇒10y+y-3=7(y-3+y)

⇒11y-3=7(2y-3)

⇒11y-3=14y-21

⇒-3+21=14y-11y

⇒18=3y

⇒y=6

since x=y-3

x=6-3

x=3

the no. was 10y+x=10(6)+3=60+3=63