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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. - ICSE Class 10 - Mathematics

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 Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6E | Q: 14

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Solution 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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