Question

A two - digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, it's digits are reversed. Find the number​

Answer 1

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Answer 2

Given :-

• A two digit number is 3 more than 4 times the sum of its digits.

• If 18 is added to the number its digits are reversed.

To find :-

• The required number = ?

Solution :-

Let the tens digit of the required number be x

and unit digit of the required number be y

Required number = 10x + y

According to the question,

10x + y = 4(x + y) + 3

⤇ 10x + y = 4x + 4y + 3

⤇ 10x - 4x = 4y - y + 3

⤇ 6x = 3y + 3

⤇ 6x - 3y = 3

⤇ 3(2x - y) = 3

⤇ 2x - y = $\rm\cancel\dfrac{3}{3}$

⤇ 2x - y = 1 .........................(i)

Again we have,

10x + y + 18 = 10y + x

⤇ 10x - x + 18 = 10y - y

⤇ 9x + 18 = 9y

⤇ 9x - 9y = -18

⤇9(x - y) = -18

⤇ x - y = $\rm\cancel\dfrac{-18}{9}$

⤇ x - y = -2 ..........................(ii)

On subtracting eq (ii) from eq (i),

(2x - y) - (x - y) = 1 - (-2)

⤇ 2x - x - y - (-y) = 1 + 2

⤇ x - y + y = 3

⤇ x = 3

Putting the value of x in equation (i),

2x - y = 1

⤇ 2 × 3 - y = 1

⤇ 6 - y = 1

⤇ -y = 1 - 6

⤇ -y = -5

⤇ y = 5

Required number = 10x + y

Required number = 10 × 3 + 5

Required number = 30 + 5

Required number = 35

Hence,the required number will be 35.