10 grade maths> The sum of a two digit number and the num...

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?

veera vivek , 10 Years ago

Grade 11

4 Answers

SHAIK AASIF AHAMED

Last Activity: 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

askIITians faculty

Approved

AnshulJadhav

Last Activity: 7 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

Last Activity: 7 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

Last Activity: 7 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...