Question

the sum of a number of 2 digit and of the number formed by reversing the digits is 110 and the difference of the digit is 6 find the number​

Answer 1

Answer:

No. formed is 82

Step-by-step explanation:

GIVEN-

Two no(s) with difference of their digit = 6

TO FIND-

The number

SOLUTION-

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

Now ,

The no. formed = 10x + y

Now , on reversing , the no. becomes = 10y + x

So , ATQ -

→10x + y + 10y + x = 110

→11x + 11y = 110

→11 ( x + y ) = 110

→ x + y = $\dfrac{110}{11}$

→ x + y = 10 ------- eq (1)

→ $\Large\boxed{x + y = 10}$

Also , it is given -

x - y = 6 -------- eq (2)

♦ SOLVING EQUATION (1) AND (2)

Add both the equations.

x + y + x - y = 10 + 6

2x = 16

x = $\dfrac{16}{2}$

$\large\bold{x = 8}$

Now , substitute in eq ( 2 )

→ x - y = 6

→ 8 - y = 6

→ y = 8 - 6

$\large\bold{y = 2}$

• The no. formed is - 10x + y = 10(8) + 2 = 80 + 2 = 82