Civil Services Examination · Question 29
Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR - PS = PPT. If Q = 3 and T < 6, then what is the number of possible values of (R, S)?
Show answer & explanation
Answer: (B) 3
Explanation
100P + 10Q + R - (10P + S) = 110P + T gives 10Q + R - S - T = 20P. With Q = 3 only P = 1 works, so S + T = R + 10 with T < 6 and all digits distinct and non-zero: (R, S, T) = (2, 8, 4), (2, 7, 5), (4, 9, 5). That gives 3 values of (R, S). (Answer as per the official UPSC answer key.)