Question

the sum of a number of two digits and of the number formed by reversing the digit is110, and the difference of digits is 6. find the number.​

Answer 1

Answer:

28 or 82

Step-by-step explanation:

Let the unit digit be b and tens digit be a( a > b ). So the number should be ab, ab can be also be written as 10a + b. And when digits are reversed new no. is ba which can be written as 10b + a.

 Here, sum of or. no. and new. no is 110

⇒ ( 10a + b ) + ( 10b + a ) = 110

⇒ 10a + b + 10b + a = 110

⇒ 11a + 11b = 110

⇒ 11( a + b ) = 110

⇒ a + b = 10          ...( 1 )

   Also, difference of digits is 6 :

                  ⇒ a - b = 6

   Adding ( 1 ) and a - b:

⇒ ( a + b ) + ( a - b ) = 10 + 6

⇒ a + b + a - b = 16

⇒ 2a = 16

⇒ a = 8

        Hence,

           a - b = 6

           ⇒ 8 - 6 = b = 2

Hence the required number is ab or 82.

However number can be either 82 or 28.

Answer 2

★ Question ★

→the sum of a number of two digits and of the number formed by reversing the digit is110, and the difference of digits is 6. find the number.

★ Answer.

→ let the once place digit = a tens=b,

so,

→ number = 10b+a

→ reverse of the number is 10b+a

→ difference of the digit = a-b=6 or a= 6+b

★ According to question.

→ 10b+a+10a+b=110

→ 11 (a+b) =110

→ a+b=110/11

→ a+b= 10

→ 6+b+b=10

→ 2b=10-6

→ 2b=4

→b=4/2=2

→a=6+2

→ a=8

hence number is 28.

and b=6+1

then number is 82.