Question

The sum of the digits of a two digit no. is 7 if 27 is subtracted from it, the digits are reversed find the product

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Answer 1

hi

simple trick : 27/9=3

so the difference between digits is of 3

let the smaller one be x

then other is x+3

x+x+3=7

x=2

so the no. is 52

Answer 2

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)

Substituting value of y from equation (2) in equation (1)

x + x+3 = 7

2x + 3 = 7

2x =4

x= 2

Substituting x= 2 in equation (2)

y= 5

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.