Example 13 : The sum of a two-digit number and the number obtained by

1.	Example 13 : The sum of a two-digit number and the number obtained by reversinguchthe digits is 66. If the digits of the number differ by 2, find the number. How many snumbers are there?
Answer» Let the unit digit be X and ten 's digit be Y. So, original digit be ( X+10.Y) , And by reversing the digit we get (Y+10.x) SO ACCORDINGTO THE QUESTION (X+10Y)+(Y+10X) = 66 11X+11Y = 66 11(X+Y) = 66 X+Y = 66/11 X+Y = 6 ------------------- 1 And, since digits differ by 2 So, X-Y = 2 --------------- 2 Adding 1 and 2 equations we get 2X = 8 X = 8/2 so, X = 4 And, puttingvalue of Xin equation 1 X + Y = 6 4 + Y = 6 Y = 6 - 4 Y = 2 Therefore, number is given by putting value of X & Y Hence, number is ( 4+10*2) = 24... Like my answer if you find it useful!

Example 13 : The sum of a two-digit number and the number obtained by reversinguchthe digits is 66. If the digits of the number differ by 2, find the number. How many snumbers are there?

Answer»

Let the unit digit be X and ten 's digit be Y. So, original digit be ( X+10.Y) , And by reversing the digit we get (Y+10.x)

SO ACCORDINGTO THE QUESTION

(X+10Y)+(Y+10X) = 66

11X+11Y = 66

11(X+Y) = 66

X+Y = 66/11

X+Y = 6 ------------------- 1

And, since digits differ by 2

So, X-Y = 2 --------------- 2

Adding 1 and 2 equations we get

2X = 8

X = 8/2

so, X = 4

And, puttingvalue of Xin equation 1

X + Y = 6

4 + Y = 6

Y = 6 - 4

Y = 2

Therefore, number is given by putting value of X & Y

Hence, number is ( 4+10*2) = 24...

Like my answer if you find it useful!