Question

5) A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this
number, the sum is equal to the number obtained by interchanging the digits. Find the
number.
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Answer 1

Let the number be 10x+y

Sum of digits=x+y

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

10x+y=4x+4y+3

10x-4x+y-4y=3

6x-3y=3

3(2x-y)=3

(2x-y)=1

2x=y

10x+y+18=10y+x

18=10y-y+x-10x

18=9y-9x

18=9(y-x)

2=y-x

2+x=y

2+x=2x

2=2x-x

x=2

y=4

Therefore the number is 24.

Answer 2

Answer.

Let x and y be units and tens digits of the number.

So, number = 10y + x

According to question,

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

⇒ 10y + x = 4x + 4y + 3

⇒ 10y – 4y + x – 4x = 3

⇒ 6y – 3x = 3

⇒ 2y – x = 1 …(1)

Now, number obtained by reversing the digits = 10x + y

∴ 10y + x + 18 = 10x + y

⇒ 10y – y + x – 10x = –18

⇒ 9y – 9x = –18

⇒ y – x = –2 …(2)

Subtracting (2) from (1), we get,

y = 3

Put y = 3 in equation (2),

3 – x = –2

⇒ x = 3 + 2

⇒ x = 5

Hence, the number is 10 × 3 + 5 = 35.

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