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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

Sum

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.

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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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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 6 Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6 (E) | Q 14 | Page 79
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