Question

A two digit number increases its value by 27 when we change places of digits If the sum of digits is 7. Find the number​

Answer 1

Your Answer:

Given:-

• A two digit number increases its value by 27 when we change places of digits
• The sum of digits is 7

To find:-

• The original number

Solution:-

Let the number at unit digit be y and at the tens place be x

ATQ,

$\tt 10x+y+27=10y+x\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow(1)\\\\ \tt and\\\\ \tt x+y=7\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow(2)$

$\tt Solving\:eq\:(1) \\\\ \tt 10x+y+27=10y+x\\\\ \tt \Rightarrow 9x-9y=-27\\\\ \tt \Rightarrow x-y=-3\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow(3)$

From equation 2 and 3

x=5

and

y=2

So, the number is

$\tt 10x+y\\\\\tt =10(5)+2\\\\=50+2\\\\ \tt =52$