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# A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.

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This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
This is an important ques

A two digit number contains the bigger at ten’s place.

The product of the digits is 27 and the difference between two digits is 6.

Find the number.

Question no. 11, ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

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1. Let us consider unit’s digit be ‘x’

Ten’s digit = x+6

Number = x + 10(x+6)

= x + 10x + 60

= 11x + 60

So according the question,

x(x + 6) = 27

x2 + 6x – 27 = 0

let us factorize,

x2 + 9x – 3x – 27 = 0

x(x + 9) – 3 (x + 9) = 0

(x + 9) (x – 3) = 0

So,

(x + 9) = 0 or (x – 3) = 0

x = -9 or x = 3

so, value of x = 3 [since, -9 is a negative number]

∴ The number = 11x + 60

= 11(3) + 60

= 33 + 60

= 93

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