Question

a 2-digit number is 6 more than 4 times the sum of its digits if 27 is added to the number its digit are reversed
find the number

Answer 1

Let the no. Be 10a + b

Sum of digits = a+b

According to question
10a +b =4(a+b) + 6
=> 10a +b = 4a +4b + 6
=> 6a - 3b = 6
=> 2a - b = 2 ------------(1)


Original no. + 27 = Reversed no.
10a +b +27 = 10b+a
=> 9a - 9b = - 27
=> a - b = - 3 ----------(2)


On subtracting equation 2 from 1, we get
2a - b - a + b = 2-(-3)
=> a = 5
On putting the value of a in equation 2,we get
5-b = - 3
=> b = 5+3
b = 8


Required no. = 58


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