Question

. Find the original number if the sum of digit and the number obtained by interchanging th
digits are as follows:
(ii) 7, 27 more than the original number​

Answer 1

Answer:

• 25

Given :

• Sum of the digits = 7
• Number obtained by interchanging the digit = 27 more than original number .

To find:

• Original number

Solution :

Let the digit at ones place be x and at tens place be y .

Then , the original number becomes 10y + x .

A/Q ,

y + x = 7

y = 7-x .

Number formed after interchanging the digits = 10x + y .

A/Q ,

New number = 27 + original number

10x + y = 27 + 10y + x

10x + 7 - x = 27 + 10 (7-x) + x

9x +7 = 27 + 70 - 10x + x

9x +10x - x = 27 + 70 -7

18x = 90

x = 90/18

$\implies$ x = 5

$\implies$ y = 7-5 = 2

So , the original number is 10×2 + 5

= 20+5

= 25

New number = 52

$\boxed{ \therefore \sf \: original \: number = 25} \\ \\ \tt \: and \\ \\ \boxed{ \therefore \sf \: new \: number = 52}$

Verification :

New number- original number

= 52 - 25

= 27

Hence verified