a two digit number is 4 times to its sum of digits, when 9 is added to the number the digits will get reversed then what is that number

Dear student,

Lrt the 2 digit number be 10x+y

10x+y=4x+4y

6x=3y

2x=y

Now,

10x+y+9=10y+x

9x-9y=-9

x-y=-1

On solving we get

x=1

y=2

Number is : 10x+y=12

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

sagarsingh24.iitd@gmail.com

the number is 12 .

12 = 4* ( 1+2)

12 + 9 = 21, which is reverse the number

2 digit number is 10x+y where x is tens place and y is units place

so

according to the question

10x + y = 4 (x+y)

solving it we get

6x-3y = 0 ------------------------(i)

the second part of the question says 9 is added to the number and then number obtained is the original numbers reverse

so

10x + y + 9 = 10y + x

solving we get

9x-9y=-9

==>  x - y = -1 --------------------------(ii)

multiplying (i) by 1 and  (ii) by 3 and subtracting (i) from (ii) we get

-3x = -3

==> x=1 ------------- (iii)

substituting this in any of the equations (i) or (ii) we can find y

y = 2

so the original number is 10x + y = 10*1 + 2 = 12

reversed number = 21 !

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