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A Two Digit Positive Number is Such that the Product of Its Digits is 6. If 9 is Added to the Number, the Digits Interchange Their Places. Find the Number. - ICSE Class 10 - Mathematics

ConceptFactorising a Polynomial Completely After Obtaining One Factor by Factor Theorem

Question

A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.

Solution

Let the digit at the tens place be ‘a’ and at units place be ‘b’.

The two-digit so formed will be 10a + b.

According to the first condition, the product of its digits is 6.

⇒ a x b =6

=> x = 6/b ...(1)

According to second condition

10a + b + 9 = 10b + a

⇒ 9a - 9b = 9

=> a - b = 1

=> a - 6/a= 1    From  1

=> a^2 - a - 6 = 0

=> (a - 3)(a + 2) = 0

=> a= -3 or 2

Since a digit cannot be negative, a = 2.

=> b = 6/a = 6/2 = 3`

Thus, the required number = 10a + b = 10(2) + 3 = 23

Is there an error in this question or solution?

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2013-2014 (March) (with solutions)
Question 10.1 | 4.00 marks
Solution A Two Digit Positive Number is Such that the Product of Its Digits is 6. If 9 is Added to the Number, the Digits Interchange Their Places. Find the Number. Concept: Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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