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In a Two-digit Number, the Ten’S Digit is Bigger. the Product of the Digits is 27 and the Difference Between Two Digits is 6. Find the Number. - Mathematics

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Question

In a two-digit number, the ten’s digit is bigger. The product of the digits is 27 and the difference between two digits is 6. Find the number.

Solution

Given, the difference between the two digits is 6 and the ten’s digit is bigger than the unit’s digit.
So, let the unit’s digit be x and ten’s digit be (x + 6).
From the given condition, we have:
x(x + 6) = 27
x² + 6x – 27 = 0
x² + 9x – 3x – 27 = 0
x(x + 9) – 3(x + 9) = 0
(x + 9) (x – 3) = 0
x = -9, 3
Since, the digits of a number cannot be negative. So, x = 3.
Unit’s digit = 3
Ten’s digit = 9
Thus, the number is 93.

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 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(E) | Q: 14 | Page no. 79
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In a Two-digit Number, the Ten’S Digit is Bigger. the Product of the Digits is 27 and the Difference Between Two Digits is 6. Find the Number. Concept: Quadratic Equations.
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