Question

Seven times a two-digit number is equal to four times the number obtained by interchanging the digits, and the digit in units place exceeds digit at 10's place by 3. Find the number

Answer 1

Answer:

36

Step-by-step explanation:

let the number in tens place be x

let the number in unit place be y

the number is 10x + y

y = x + 3

x = y - 3

x - y = -3 equ (1)

$7(10x + y) = 4(10y + x) \\ 70x + 7y = 40y + 4x \\ 70x + 7y - 40y - 4x = 0 \\ 66x - 33y = 0 \\ 11(6x - 3y) = 0 \\ 6x - 3y = 0 \: \: \: \: equ \: (2)$

x - y = -3 equ (1)

multiply with 6

6x - 6y = -18. equ (3)

subtract (3) - (2)

$6x - 6y = - 18 \\ 6x - 3y = 0 \\ we \: get \\ - 3y = - 18 \\ 3y = 18 \\ y = \frac{18}{3} = 6 \\ x = y - 3 \\ x = 6 - 3 \\ x = 3 \\ therefore \: the \: number \: is \\ = 10x + y \\ = 10(3) + 6 \\ = 30 + 6 \\ = 36$