the sum of the digits of atwo digits number is 7 if the digits are interchanged we get a two digit number which is 27more than the intial number what is the number?
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Suppose the two digit original number is 10x+y.
Suppose the two digit original number is 10x+y.(x is at tens place so multiple by 10 and y is at unit place so left as is, you may multiply it by 1 to get a clear picture but 1y is represented as y only)
Suppose the two digit original number is 10x+y.(x is at tens place so multiple by 10 and y is at unit place so left as is, you may multiply it by 1 to get a clear picture but 1y is represented as y only)The sum of digits of original number is 7 →x+y = 7 —equation(1)
If 27 is added to original number its digits are interchanged .So, 10x + y +27 =10y+ x → 9x +27 = 9y → 9(x+3) = 9(y) → x+3 = y — equation(2)
If 27 is added to original number its digits are interchanged .So, 10x + y +27 =10y+ x → 9x +27 = 9y → 9(x+3) = 9(y) → x+3 = y — equation(2)Substituting value of y from equation (2) in equation (1)
x + x+3 = 7
x + x+3 = 72x + 3 = 7
x + x+3 = 72x + 3 = 72x =4
x + x+3 = 72x + 3 = 72x =4x= 2
x + x+3 = 72x + 3 = 72x =4x= 2Substituting x= 2 in equation (2)
x + x+3 = 72x + 3 = 72x =4x= 2Substituting x= 2 in equation (2)y= 5
So original number is 10 (2) + 5 i.e. 20 +5 → 25.
So original number is 10 (2) + 5 i.e. 20 +5 → 25.In order to check the answer.. 25 is original number and 52 is the number formed by interchanging the digits.
So original number is 10 (2) + 5 i.e. 20 +5 → 25.In order to check the answer.. 25 is original number and 52 is the number formed by interchanging the digits.25 +27 = 52.