number obtained by interchang the digits of a two-digit number is more than the original number by 27 and the sum of the digits is 13 what is the original number
Answer (1)
16th Dec, 2019
Let the actual number be 10x+y.
Number on exchanging the digits will be 10y+x.
Now, 10y+x = 10x+y+27
=> 9y = 9x+27
Dividing the equation by 9.
y = x+3 (eqn i)
According to the question, x+y = 13
=> y = 13-x (eqn ii)
From eqn i and ii:
13-x = x+3
=> 10 = 2x
=> x = 10/2 = 5
Putting the value of x in eqn i:
y = x+3 = 5+3 = 8
Therefore the actual number was 10x+y = 10(5)+8 = 50+8 = 58.
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