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UPSC Prelims

Mathematics

Theme:

Number System / संख्या पद्धति

Q66 2022, Number System

Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If pq = 2430 then what is the difference between p and q?

मान लीजिए p दो अंकों की एक संख्या है और q उन्हीं अंकों को उलटे क्रम में लिखने से बनी संख्या है। यदि pq = 2430 तो p और q के बीच का अन्तर क्या है?

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The product of two, two digits numbers has one 0 in it. That means the unit digit of one of the numbers must be equal to 5.

As the number is a two digit one then it will be of form 5_ × _ 5 = 2430.

To get zero the other digit must be an even number

Possible cases are 2 and 4

52 × 25 = 1300, 54 × 45 = 2430.

Thus digit is 54. Hence, 54 – 45 = 9

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