Question

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. Find the number.​

Answer 1

Answer:

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

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.

Step-by-step explanation:

Hᴏᴘᴇ Iᴛ Hᴇʟᴘs.