Deepak Bora
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A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to 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.
Question Number 14 Exercise 3E of RS Aggarwal Solution
Here A two-digit number is n more than n times the sum of its digits. If a number is added to the number,
the digits are reversed.
You have to find the number.

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  1. Solution :-
    Let the tens and the units digits of the required number be x and y
    Number = (10x + y)
    According to the Question,
    ⇒ 10x + y = 4(x + y) + 3
    ⇒ 10x + y = 4x + 4y + 3
    ⇒ 6x – 3y = 3
    ⇒ 2x – y = 1 ….(i)
    also, 10x + y + 18 = 10y + x
    ⇒ 9x – 9y = -18
    ⇒ x – y = -2 ….(ii)
    Subtracting (ii) from (i), we get
    ⇒ x = 3
    Putting x’s value in (i), we get
    ⇒ 2x – y = 1
    ⇒ 2 × 3 – y = 1
    ⇒ y = 6 – 1
    ⇒ y = 5
    Number = (10x + y) = 10 × 3 + 5 = 30 + 5 = 35.
    Hence, the required number is 35.

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