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

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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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Let the number be “ab”

Now ab can be written as “10a+b”

Condition 1 :

10a+b =4(a+b)+3

=>10a+b=4a+4b+3

=> 6a=3b+3

=> 2a=b+1 ————equation (1)

Condition 2 :

Reversed number “ba” =10b+a

10a+b+18= 10b+a

=>9a+18=9b

=>a+2=b ————equation (2)

Compare both the equations

We get a=3,b=5

Therefore the required two digit number is 35