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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
10x + y + 9 = 10y + x
solving we get
==> 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 !
please approve if you like the answer
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