a two digit number is 3 more than 4 times the sum of its digits if 18 is added to the number its digits are reversed find the number
a two digit number is 3 more than 4 times the sum of its digits if 18 is added to the number its digits are reversed find the number
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Let, the two digits at tens and ones places are a and b respectively.
Then, the number is (10a + b).
When the digits are reversed, the number becomes (10b + a).
By the given condition,
the original number = 4(sum of the digits) + 3
=> 10a + b = 4(a + b) + 3
=> 10a + b = 4a + 4b + 3
=> 6a = 3b + 3
=> 2a = b + 1 .....(i)
and
the original number + 18 = the reversed digits number
=> 10a + b + 18 = 10b + a
=> 9a + 18 = 9b
=> a + 2 = b .....(ii)
Now, from (ii) b = a + 2 is got and putting this in (i), we get
2a = a + 2 + 1
=> a = 3
Putting a = 3 in (ii), we get
b = 3 + 1
=> b = 5
So, the original number is
= 3×10 + 5
= 30 + 5
= 35
and
the reversed digits number is
= 5×10 + 3
= 50 + 3
= 53
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