Question

The sum of the digit of a two digit no is 7 and if 9 is added to the number, the digit are reversed. Find the number

Answer 1

Answer:

34

Step-by-step explanation:

Let the ten's place digit be x and one's place digit be y

We know that a two digit number is of form

10×Ten Place Digit + One Place Digit

∴ Our Original number = 10x + y

and number made by reversing the digits = 10y + x

Now, given that

Sum of digits = 7

∴ x + y = 7

or x = 7 - y -------- ( i )

According to Question

9 + Original number = number formed by reversing the digits

∴ 9 + 10x + y = 10y + x

9x - 9y = - 9

Dividing both sides by 9

x - y = -1

Putting value of x from ( i )

(7 - y) - y = -1

7 - 2y = -1

- 2y = -8

y = 4

Putting value of y in ( i )

x = 7 - y

x = 7 - 4

x = 3

∴ number = 10x + y

                = 10×3 + 4

                = 34

Check : Sum of digits: 4+3 = 7

Also 34 + 9 = 43 (digits reversed)

Answer 2

Let first digit be x and second digit be y .

Let original no be = 10 x X + Y

A/Q

1. X + Y = 7

X= 7-Y

2. 10 x X + Y + 9 = 10 x Y + X

10X + Y + 9 = 10Y + X

10X - X + 9 = 10Y - Y

9X + 9 = 9Y

9X - 9Y = -9

X - Y = -1

7-Y-Y = -1

-2Y = -1- -7

-2Y = -8

Y = 4

X = 7-4

= 3

Original no = 34

HOPE IT HELPS!!!