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# A number consisting of two digits is seven times the sum of its digits. When 27 is substracted from the number, the digits are reversed. Find the number.

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This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for
ICSE & CBSE Board.
In this question a number consisting of two digits is n times the sum of its digits. when the given number is
substracted from the number, the digits are reversed.
You have to find the number.
This is the Question Number 12 Of Exercise 3E of RS Aggarwal Solution.

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1. Let the tens and the units digits of the required number be x and y, respectively.

Required number = (10x + y)

10x + y = 7(x + y)

10x + 7y = 7x + 7y or 3x – 6y = 0 ……….(i)

Number obtained on reversing its digits = (10y + x)

(10x + y) – 27 = (10y + x)

⇒10x – x + y – 10y = 27

⇒9x – 9y = 27  ⇒9(x – y) = 27

⇒x – y = 3 ……..(ii)

On multiplying (ii) by 6, we get:

6x – 6y = 18 ………(iii)

On subtracting (i) from (ii), we get:

3x = 18

⇒ x = 6

On substituting x = 6 in (i) we get

3 × 6 – 6y = 0

⇒ 18 – 6y = 0

⇒ 6y = 18

⇒ y = 3

Number = (10x + y) = 10 × 6 + 3 = 60 + 3 = 63

Hence, the required number is 63.

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