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Question

A two-digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.


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Solution

Step 1: Assuming the two-digit number and writing in equation form:

let us assume two digits bePQ.

As per the condition given in the question,

Product of two-digits is18, PQ=18 … [equation (i)]

63 is subtracted from the number, the digits interchange their places,

PQ63=QP … [equation (ii)]

Now, assume a two-digit number bePQ, means P=10P (as it comes in tens digit)

Then, PQ63=QP

10P+Q63=10Q+P

By transposing we get,

9P9Q63=0

Divide both sides by 9,

PQ7=0 … [equation(iii) ]

So, PQ=18

P=18Q

Substitute the value of P in equation(iii),

Step 2: Making and simplifying quadratic equation:

18QQ7=018Q27Q=0Q2+7Q18=0Q2+9Q2Q18=0Q(Q+9)2(Q+9)=0Q+9=0andQ2=0Q=-9andQ=2

Hence, Q=2 [Since the value of Q cannot be negative]

Then, P=18Q

P=182P=9

Hence, the required two-digit number is 92.


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