# 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