Pls solve this problem...

Solution:
$$\begin{gathered} P P Q \\ \times Q \\ \overline{ R Q 5 Q } \end{gathered}$$

⇒ Q × Q has the last digit Q.

⇒ Q = 1, 5 or 6

 When Q = 1, P × Q = Q

⇒ P × 1 = 1 ⇒ P = 1

as P and Q are 2 different numbers

∴ P ≠ 1 Q ≠ 1

Now when Q = 5

5P + 2 has the last digit 5 which is not possible

∴ Q = 6

When Q = 6,  6 P + 3 has the last digit 5.

⇒ P = 2 or 7

 if P = 2

226 × 6 has last 3 digits 356

∴ P ≠ 2 and P = 7

⇒ R = 4

 ∴ P = 7, Q = 6 and R = 4

⇒ P + Q + R = 7 + 6 + 4 = 17