Question

In a number of two digits the sum of the digits is 7. If27 is
added to the number the digits are reversed. Find the
number​

Answer 1

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

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.

DEADSOUL

Answer 2

Answer:

two digit no. is 10x+y

A.T.Q.

x+y = 7 => (1)

also,

when digit interchanged no.is =>

10y+x

10x+y+27=19y+x

9x-9y= -27

9(x-y)= -27

x-y= -3 => (2)

Adding (1) & (2) ==>

x+y = 7

x-y = -3

2x = 4

x= 2

x+y = 7

2+y = 7

y= 7-2

y = 5

10x+y => 10×2 +5 = 25

hence the no.is 25

its the answer.....