# The sum of a two digit number and the number obtained by reversing the digits is 66.if the digits of the number differ by 2,find the number.how many such numbers are there?

SHAIK AASIF AHAMED
10 years ago

Hello student,

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...

There are manysuch numbersdepending on equation!

Thanks and Regards

Shaik Aasif

11 Points
6 years ago
Let the tens place number be X and the units place number be Y. So, the original number will be 10X+Y and the reversed number will be 10Y+XAccording to first condition:-(10X+Y)+(10Y+X)=6611X+11Y=66X+Y=6...........(1)According to second condition:-X-Y=2............ (2)Substract equation (2)from(1) X+Y=6 -X-Y=2 ___________ 2Y=4Therefore Y=2 Put Y=2 in equation (1) X+2=6 Therfore,X=4So, the number will be 42 or 24So hope that you got the solution...!!!!Regards Anshul JadhavClass 10 student
Divyansh Singh
13 Points
6 years ago
Let unit digit be xAnd that of yen`s digit be 10yATQ-1x+10y+y+10x=6611x+11y=6611(x+y=6)x+y=6------1 eqATQ-2x-y=2-------2eqFrom eq 1 and 2 we obtain(by elimination)x=4y=2No.x+10y 4+10×2 = 4+20 = 24 ......required no..
Vivek
70 Points
6 years ago
Hello student,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) = 6611X+11Y = 6611(X+Y) = 66X+Y = 66/11X+Y = 6 ------------------- 1And, since digits differ by 2So, X-Y = 2 --------------- 2Adding 1 and 2 equations we get2X = 8X = 8/2so, X = 4And, puttingvalue of Xin equation 1X + Y = 64 + Y = 6Y = 6 - 4Y = 2Therefore, number is given by putting value of X & YHence, number is ( 4+10*2) = 24...