Question

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Answer 1

Answer:

Original number = 25

Solution:

Let the 2 digits of the number be x and y.

★ According to the question,

x + y = 7 ----- [Equation 1]

Original number:

Tens | Units

x | y

Value → 10x + y

When number is interchanged: (new number)

Tens | Units

y | x

Value → 10y + x

Now, from Question;

New number = 27 + Original number

⇒ 10y + x = 27 + 10x + y

⇒ 10y - y = 27 + 10x - x

⇒ 9y = 27 + 9x

⇒ 9y - 9x = 27

⇒ y - x = 3

⇒ -x + y = 3 ----- [Equation 2]

Add Equation 1 and 2 to eliminate the x term.

x + y = 7

{+} - x + y = 3

2y = 10

⇒ y = 10 ÷ 2

⇒ y = 5

Now substitute the value of y in Equation 1 to find out the value of x.

x + y = 7

➝ x + 5 = 7

➝ x = 7 - 5

➝ x = 2

We know that value of original number is (10x + y) from above.

So, Original number = 10x + y

➵ Original number = 10(2) + 5

⇢ Original number = 25

∴ Original number = 25