Assertion (A): In a two digit number, three times the digit at ten's place is equals to two times the digit at the unit place and the sum of the digit is 5 then for number 10x + y, 3x = 2y and x + y = 5.

Reason (R): The number is 32.

1. A is true, but R is false.

2. A is false, but R is true.

3. Both A and R are correct, and R is the correct explanation for A.

4. Both A and R are correct, and R is not the correct explanation for A.

Let the two digit number be 10x + y.

It is given that three times the digit at ten's place is equals to two times the digit at the unit place.

⇒ 3x = 2y

⇒ x = $\dfrac{2}{3}$ y ………………..(1)

And, the sum of the digit is 5.

⇒ x + y = 5 ……………………(2)

So, assertion (A) is true.

Substitute the value of x from equation (1) in equation (2), we get :

$\Rightarrow \dfrac{2}{3}y + y = 5\\[1em] \Rightarrow \dfrac{2y + 3y}{3} = 5\\[1em] \Rightarrow \dfrac{5y}{3} = 5\\[1em] \Rightarrow y = \dfrac{5 \times 3}{5}\\[1em] \Rightarrow y = 3$

Substituting the value of y in equation (1),

⇒ x = $\dfrac{2}{3} \times 3$

⇒ x = 2

Thus, the number is 10x + y = 10(2) + 3 = 23.

So, reason (R) is false.

∴ A is true, but R is false.

Hence, option 1 is the correct option.