Question

A number consists of two digits whose sum is 8. If 18 is added to the
number, its digits are interchanged. The number is

Answer 1

Answer:

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Step-by-step explanation:

Let us assume that one of the digit of the two digit number is X, then problem the other number will be (8 - X)

From problem we get that, if we add 27 to the number the digits get interchanged and also since the number is a two digit number then X will in tens place (7 - X) will be in ones place.

So the equation we get

10X + (8 - X) + 18 = 10(8 - X) + X

10X + 8 - X + 18 = 80 -10X + X

9X + 26 = 80 - 9X

9X + 9X = 80 - 26

18X = 54

X = 54/18

X = 3,

So the digit in tens place = 3 the digit in ones place is (8 - 3 = 5) , then the number is 35 and when 18 is added the result is 53, the digits interchange their position in the new number.

Ans: 35.

Hope this helps !!

Answer 2

Answer:

35

Step-by-step explanation:

Let the ten's place of the number be x and unit's place of the number be y.

According to the question,

x + y = 8              .....(1)

Original number = x(10) + y(1) = 10x + y

Reversed number = y(10) + x(1) = 10y + x

According to the second part of the question,

10x + y + 18 = 10y + x

9x - 9y = -18

9(x - y) = -18

x - y = -2            ......(2)

In equation (1),

x + y = 8

x = 8 - y               .......(3)

Now, we will substitute the value of x in the equation (2),

x - y = -2

8 - y - y = -2

8 -2y = -2

-2y = -10

y = 5

Now, we will substitute this y value in (3),

x = 8 - 5

x = 3

Therefore, the original number is 3(10) + 5(1) = 30 + 5 = 35

Hope this helps you!!!