Question:
product of two no is 30 when 9 is subtracted from no it will interchanged the digit find the no
Answer:
Let the two digit number is 10x + y
Given, the product of its digits = 30
=> xy = 30 ............1
Again, when 9 is subtracted from the number, the digits interchange their places
=> 10x + y - 9 = 10y + x
=> 10x + y - 10y - x = 9
=> 9x - 9y = 9
=> 9(x - y) = 9
=> x - y = 9/9
=> x - y = 1 .............2
Now, (x + y)2 = (x - y)2 + 4xy
=> (x + y)2 = 12 + 4 * 30
=> (x + y)2 = 1 + 120
=> (x + y)2 = 121
=> x + y = √121
=> x + y = ±11
Case 1. when x - y = 1 and x + y = 11
After solving it, we get
x = 6, y = 5
Case 2. when x - y = 1 and x + y = -11
After solving it, we get
x = -5, y = -6, wehich is not possible.
So, x = 6, y = 5
So, the number = 10*6 + 5
= 60 + 5
= 65
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