Question

A number consists of two digits. the sum of the digits is 7 if 27 is added the digits are reversed. find the number

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Answer 1

Answer:

Step-by-step explanation:

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

2 x + 3 = 7

2 x = 4

x = 2

Substituting x = 2 in equation (2)

y = 5

So original number is 10 (2) + 5 i.e. 20 +5 = 25.

25 is original number and 52 is the number formed by interchanging the digits.

25 + 27 = 52.

Answer 2

$x+y=7\\10x+y+27=10y+x\\\\x+y=7\\9x-9y=-27\\\\x+y=7\\\underline{x-y=-3}\\2x=4\\x=2\\\\2+y=7\\y=5\\\\10\cdot2+5=25$

25