Question

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BRIEFLY explain krna plz​

Answer 1

Step-by-step explanation:

Hint:

At first let's assume the two digit number to be 10x+y and by the the condition the sum of the digits is 9, we get x+y=9 and by using the condition that when the digits are interchanged twice the new number is nine times the original number we get 8x−y=0.Now we need to solve this pair of linear equations using substitution method and find the value of x and y.

Complete step by step solution:

We need to find a two digit number

Let the two digit number be 10x+y

In the first condition , we are given that the sum of the digits is 9

⇒x+y=9 …………..(1)

The next condition states that when the digits are interchanged two times the new number is nine times the original number

That is ,

⇒2(10y+x)=9(10x+y)⇒20y+2x=90x+9y⇒90x+9y−20y−2x=0⇒88x−11y=0

Dividing by 11 we get

⇒8x−y=0 ………..(2)

Now we have a pair of linear equation and hence we can solve it using substitution method

From (1) we have x=9−y

Substituting this (2) we get

⇒8(9−y)−y=0⇒72−8y−y=0⇒−9y=−72⇒9y=72⇒y=729=8

Substituting the value of y in (1) we get

⇒x+8=9⇒x=9−8⇒x=1

Using the values of x and y we get our two digit number to be

⇒10(1)+8⇒10+8⇒18

Hence the two digit number is 18

Answer 2

Given that :

• Sum of digits of two-digit number is 9
• 9 times of two - digit number is twice the number obtained by reversing the order of the digits

To Find :

• Find the original number.

Solution :

Let , the unit digit of a number = x

and the tens digit of the number = y

Then , the number = 10y + x

Reversed number = 10x + y

We are given that,

→ x + y = 9 ____(1)

We are also given that,

→ 9 (10y + x) = 2 (10x + y)

→ 90y + 9x = 20x + 2y

→ 90y + 9x - (20x + 2y) = 0

→ 90y + 9x - 20x - 2y = 0

→ 88y - 11x = 0 ____(2)

Multiply Equation (1) by 11

→ 11 (x + y) = 11 (9)

→ 11x + 11y = 99 ____(3)

Add Equation (2) and (3)

→ 88y - 11x + 11x + 11y = 99 + 0

→ 99y = 99

→ y = 99/99

→ y = 1

Substitute the value of y in Equation (1)

→ x + y = 9

→ x + 1 = 9

→ x = 9 - 1

→ x = 8

So,

the unit digit of the number = 8

and the tens digit of the number = 1

The original number = 10y + x

→ The original number = 10(1) + 8

→ The original number = 10 + 8

→ The Original Number = 18