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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