Q. In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q-S= 2S and T=R+S+3, then what is the value of P+R-T?
a) 1
b) 2
c) 3
d) Cannot be determined due to insufficient data
Correct answer: b) 2
Question from UPSC Prelims 2024 CSAT
Explanation :
Let’s determine the values of P, Q, R, S, and T based on the given conditions and the available numbers: 4, 5, 10, 12, 15.
Step 1: Analyze the Equation Q – S = 2S
This simplifies to:
Q = 3S
We need to find pairs (S, Q) where Q is three times S and both are among the available numbers:
– If S = 4, then Q = 12 (valid)
– If S = 5, then Q = 15 (valid)
– S = 10 would give Q = 30 (invalid)
– S = 12 would give Q = 36 (invalid)
– S = 15 would give Q = 45 (invalid)
So, the possible pairs are (S, Q) = (4, 12) or (5, 15).
Step 2: Analyze the Equation T = R + S + 3
Case 1: S = 4 and Q = 12
Substitute S = 4 into the equation:
T = R + 4 + 3 = R + 7
The remaining numbers are 5, 10, 15:
– If R = 5, then T = 12 (already assigned to Q, invalid)
– If R = 10, then T = 17 (invalid)
– If R = 15, then T = 22 (invalid)
This case yields no valid solution.
Case 2: S = 5 and Q = 15
Substitute S = 5 into the equation:
T = R + 5 + 3 = R + 8
The remaining numbers are 4, 10, 12:
– If R = 4, then T = 12 (valid)
– If R = 10, then T = 18 (invalid)
– If R = 12, then T = 20 (invalid)
Thus, the valid assignments are:
– S = 5
– Q = 15
– R = 4
– T = 12
– P = 10 (the only remaining number)
Step 3: Calculate P + R – T
P + R – T = 10 + 4 – 12 = 2
Answer: b) 2