Question

A two digit number is 5 times the sum of its digits while the number obtained by interchanging the digits is 20% more than the original number. what is the original number?​

Answer 1

The original number would be 45.

A two digit number is 5 times the sum of its digits while the number obtained by interchanging the digits is 20% more than the original number.

We have to find the original number.

Let the two digit number be xy.

We can write it as 10x + y.

A/c to question,

    10x + y = 5(x + y)

⇒ 10x + y = 5x + 5y

⇒ 5x = 4y

⇒ x/y = 4/5

again, 10y + x = 120 %(10x + y)

⇒ 5(10y + x) = 6(10x + y)

⇒ 50y + 5x = 60x + 6y

⇒44y = 55x

⇒x/y = 4/5

Therefore we get , x = 4  and y = 5

Now the number would be 45.

Answer 2

Given:

A two digit number is 5 times the sum of its digits while the number obtained by interchanging the digits is 20% more than the original number.

To Find:

Find the original number.

Solution:

Let the two digit number be = 10x + y

according to the question,

number is 5 times the sum of the digits

therefore, 10x + y = 5( x+y)

10x +y = 5x +5y

5x - 4y = 0 ...................................(1)

number by interchanging the digits = 10y + x

acc to question, 10y + x = 1.2 ( 10x +y )

10 y +x = 12 x +1.2y

11x - 8.8y = 0................................(2)

we get x/y = 4/5

therefore x=4 and y 5

so the number would be 45.