Question

sum of the digits of a two digit number is 8 when we interchange the digits it is found that the resulting number is greater than the original number by 6.Find the numbers .​

Answer 1

Answer:

Let the tens digit=x

and units digit=y

Hence sum x+y=8…………(i)

Number =10x+y

Number formed by reversing the digits =10y+x

(10y+x)=(10x+y)+18 i . e. 9y-9x=18

Or y-x=2…………..(ii)

Adding (i) and (ii) gives 2y=10

Hence y=5

hence from (i) x=8-y=8–5=3

hence Number =35

Answer 2

Correct Question is :-

Sum of the digits of a two digit number is 9 when we interchange the digits it is found that the resulting number is greater than the original number by 63 .Find the numbers .

Given :-

Sum of the digits of a two digit number = 9

When interchanging the digits the resulting number is greater than original number by 63.

To find :-

What is the Original number and interchanged number ?

SoLuTioN :-

We consider the digit at one's place be x and digit at ten's place be y.

Now ,

Original number = x + 10y

From ...1

⇒ x + y = 9

⇒ x = 9 - y .............. (i)

Now

Interchanged number = y + 10x

So , From 2nd

✦ y + 10x = x + 10y + 63

✦ y + 10x - x - 10y = 63

✦ 9x - 9y = 63

✦ 9 (x - y) = 63

✦ 9 (9 - y - y) = 63

✦ 9 (9 - 2y) = 63

✦ 81 - 18y = 63

✦ -18y = 63 - 81

✦ y = -18 /-18

✦ y = 1

Now putting value in (i) :

✦ x = 9 - 1

✦ x = 8

Original number =

x + 10y = 8 + 10(1)

= 8 + 10 = 18

Interchanged number

= y + 10x = 1 + 10(8) = 1 + 80 = 81

We get :-

Original number is 18 and

interchanged number is 81.