Question

the sum of a two digit number and the number formed by reversing the order of digit is 66 if the two digits differ by 2 find the number how many such numbers are there​

Answer 1

The numbers are 42 and 24.

Step-by-step explanation:

Let two digit number be xy

Original number:  10x + y

Reversed number: 10y+x

Sum of original number and reversed number is 66

10x+y+10y+x=66

11x+11y=66

x+y=6   ----------(1)

Differ of two digit number by 2

|x-y|=2

make two equation

x - y = 2           or     x - y = -2

• Solve system of equation,  x + y = 6 and x - y = 2

2x = 8

x = 4 , y = 2

• Solve system of equation, x + y = 6 and x - y = -2

2x = 4

x = 2 , y = 4

Numbers are: 42 and 24

Only two possible numbers.

#BAL

Answer 2

Answer:

2

Step-by-step explanation:

Let's call the two digit number : 10a+b.

Then its reversed value is 10b+a.

Their sum is 11(a+b).

∴$a+b=6$, sum of all digits is 6.

Two digits differ by 2(A T T E N T I O N : it's absolute value.).

∴$a-b=2$ or $a-b=-2$

Let's solve it.

$(a,b)=(4,2),(2,4)$

∴Two number 42 and 24 satisfies.