Question

A two digit number is 3 more than 4 times the sum of its digit . If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.

Answer 1

Answer:

hey

Step-by-step explanation:

let units digit be y adn tens be 10x

atq,

number=10x+y

∵

(10x+y) - 4(x+y)= 3.....(i)

and

(10x+y)+ 18=10y+x.....(ii)

Solving (i)

10x+y-4x-4y=3

or,6x-3y=3

or,2x-y=1....(1)

Solving (ii)

10x+y-10y-x=-18

or, 9y-9x=18

or,y-x=2...(2)

(1)+(2)

2x-y+y-x=1+2

or,x=3

Thus, y=x+2 (from (2))

y=5

∴ the number= 10x+y=10x3+5=35

then tens digit is 10+x

Answer 2

Answer:

let units digit be y and tens be 10x

atq,

number=10x+y

∵

(10x+y) - 4(x+y)= 3.....(i)

and

(10x+y)+ 18=10y+x.....(ii)

Solving (i)

10x+y-4x-4y=3

or,6x-3y=3

or,2x-y=1....(1)

Solving (ii)

10x+y-10y-x=-18

or, 9y-9x=18

or,y-x=2...(2)

(1)+(2)

2x-y+y-x=1+2

or,x=3

Thus, y=x+2 (from (2))

y=5

∴ the number= 10x+y=10x3+5=35

then tens digit is 10+x