Question

a number of two digits of which tens digit exceeds the units digit by 3. the number is 7 times the sum ot its digits find the number.

Answer 1

Let unit digit of number be x and tens digit of the number is y.
Now the original number is 10y +x .
(Case -1)
y = x+3
so , y -x =3 _eq.1

(Case -2)
(x+y)7 =10y +x
7x +7y =10y-x
6x-3y = 0
Now elimination method,
(y-x =3)6 , (6x-3y=0)1

-6x+6y = 18
6x-3y = 0
___________
0+3y = 18

y = 6.

Now put value of y into equation 1.
6 -x = 3
-x = -3
x= 3



Therefore original number is 10(6) +3 = 63 .