A two-digit number is such that its product of its digit is . When is subtracted from the number, the digits interchange their places. Find the number.
Step 1: Assuming the two-digit number and writing in equation form:
let us assume two digits be.
As per the condition given in the question,
Product of two-digits is, … [equation ]
is subtracted from the number, the digits interchange their places,
… [equation (ii)]
Now, assume a two-digit number be, means (as it comes in tens digit)
By transposing we get,
Divide both sides by ,
… [equation ]
Substitute the value of in equation,
Step 2: Making and simplifying quadratic equation:
Hence, [Since the value of cannot be negative]
Hence, the required two-digit number is