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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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#### APPEARS IN

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

#### Video TutorialsVIEW ALL [5]

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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