Question

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

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

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QUESTION -

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

Find the number.

SOLUTION -

Let the required number be ab.

Sum of digits = a + b ........ ( 1 )

10 a + b = 4 ( a + b )

10 a + b + 18 = 10 b + a

=> 9 a + 18 = 9 b

=> a + 2 = b

10 a + a + 2 = 4 ( a + a + 2 )

=> 11 a + 2 = 8 a + 8

=> 3 a = 6

=> a = 3

=> a + 2 = 5

=>ab = 35......... [ A ]

So the number becomes 35.

ANSWER :

The original number is 35.

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