Question

3. 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

EXPLANATION.

Let the digit at tens place be = x

Let the digit at unit place be = y

original number = 10x + y

reversing number = 10y + x

A two digit number is 3 more than 4

times the sum of its digit.

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

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

=> 6x - 3y = 3

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

If 18 is added to the number it's digit

are reversed.

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

=> 9x - 9y = -18

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

From equation (1) and (2) we get,

=> x = 3

put the value of x = 3 in equation (1)

we get,

=> 2(3) - y = 1

=> 6 - y = 1

=> y = 5

Therefore,

original number = 10x + y = 10(3) + 5 = 35.

Answer 2

Answer:

Step-by-step explanation: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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