Question

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

Answer 1

Answer:-

• The original number is 35.

Step by step Explaination:-

Let

The original number in the form of

10x + y,

where x is the digit in the tenth place and y in its unit place.

When the digits are reversed the number will be in the form 10y + x.

Now According to the question,

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

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

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

=> 6x = 3 + 3y

=> 6x - 3y = 3......equation 1

Also:-

=> (10x + y)+18 = (10y + x)

=> (10x + y) - (10y + x) = -18

=> 10x + y - 10y - x = -18

=> 9x - 9y = -18

=> 9(x - y) = -18

=> (x - y) = -18/9

=> (x - y) = -2........equation 2

Now:-

=> x - y = -2

=> y = x + 2......equation 3

On putting this value of equation 3 in equation 1 we get,

=> 6x - 3y = 3

=> 6x - 3(x + 2) = 3

=> 6x -3x - 6 = 3

=> 3x - 6 = 3

=> 3x = 3+6

=> 3x = 9

=> x = 9/3

=> x = 3.

Putting the value of x in equation 2,

=> x - y = -2

=> 3 - y = -2

=> y = 3 + 2

=> y = 5

So the original number is 10x + y

that is 10 x 3 + 5 = 35.

Therefore:-

The Original number is 35.

#answerwithquality #BAL

Answer 2

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.