Question

the sum of the digits of a two-digit number is 7 if the digits are reversed the number new increased by 3 less than 4 times the original number find the original number​

Answer 1

let tens digit be x and ones digit be y

A.T.Q.

Case I

x + y = 7 -------(1)

Case II

Reversed No. = 10y+x

;

(10y+x) + 3 = 4(10x+y)

10y+x+3 = 40x+4y

10y-4y+ x - 40x = -3

39x-6y =3 ( dividing whole by 3)

13x-2y =1 ------(2)

on multiplying eq.(1) by 2

2x+2y=14----(3)

solving eq. (2) and (3) by elimination method

13x-2y =1

2x+2y =14

-------------

15x=15

x=1

putting value of x in eq. (1)

1+y=7

y=6

The required no. is 10x+y

=10×1+6

=16