Question

A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.​

Answer 1

Answer:

25

Step-by-step explanation:

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Answer 2

supposition:-

• Let the tens digit no. be x and unit digit be y

• Number = (10x + y)  

According to the Question,

⇒ $\sf 10x + y = 4(x + y) + 3$  

⇒ $\sf 10x + y = 4x + 4y + 3$  

⇒ $\sf 6x - 3y = 3$  

⇒ $\sf 2x - y = 1$ ….(i)  

2nd part of the question,

⇒$\sf 10x + y + 18 = 10y + x$  

⇒ $\sf 9x - 9y = -18$  

⇒ $\sf x - y = -2$ ….(ii)  

Subtracting (ii) from (i)

⇒ $\sf x = 3$  

Putting x's value in (i), we get  

⇒ $\sf 2x - y = 1$

⇒ $\sf 2 × 3 - y = 1$  

⇒$\sf y = 6 - 1$

⇒ $\sf y = 5$  

required Number = $\sf (10x + y) = 10 × 3 + 5 = 30 + 5 = 35.$

Hence, the required number is 35.