Q. Consider the following multiplication problem :
(PQ)×3=RQQ, where P, Q and R are different digits and R≠ 0.
What is the value of (P+R)÷Q?
(a) 1
(b) 2
(c) 5
(d) Cannot be determined due to insufficient data
Correct Answer: (b) 2
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
Problem: Find (PQ) × 3 = RQQ, where P, Q, and R are distinct digits and R ≠ 0
Step 1: Express the Equation
(10P + Q) × 3 = 100R + 10Q + Q
30P + 3Q = 100R + 11Q
30P = 100R + 8Q
15P = 50R + 4Q
Step 2: Analyze the Equation
15P – 50R = 4Q
15P ≡ 50R (mod 4)
Step 3: Find the Values
Case 1: P = 8, R = 2
15 × 8 = 120 = 50 × 2 + 4Q
120 = 100 + 4Q
4Q = 20
Q = 5
Verification:
85 × 3 = 255
This confirms P = 8, R = 2, Q = 5 are distinct digits and R ≠ 0
Step 4: Calculate (P + R)/Q
(8 + 2)/5 = 10/5 = 2
Final Answer: 2
