Q. 195.0( 1 Vote )

# A two - digit number is such that when it is multiplied by 9 then it will become double of number formed by interchanging the digits of the original number. If the difference of both the digits of the number is 7 then find the number.

Let the digit in ten’s place be x and unit’s place be y

The difference between the two digit is 7

x - y = 7

x = y + 7 …equation (i)

When the digits are multiplied the resulting number is twice formed by interchanging the digits

2×(10x + y) = 9(10y + x)

20x + 2y = 90y + 9x

11x = 88y

x = 8y

Putting the value of x from equation (i) we get

y + 7 = 8y

7y = 7

y = 1

Putting the value in equation (i) we get

x = 8

So the two digit number is 18

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