# 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 Paper

**Explanation:**

Let’s approach this step-by-step:

1) We’re given that P, Q, R, S, T represent 4, 5, 10, 12, 15, but we don’t know which is which.

2) We’re also given two equations:

Q – S = 2S

T = R + S + 3

3) From the first equation: Q – S = 2S

This can be rewritten as: Q = 3S

4) The only numbers in our set that have this relationship are 15 and 5:

15 = 3 * 5

Therefore, Q = 15 and S = 5

5) Now we know T = R + S + 3

Substituting S = 5, we get:

T = R + 5 + 3

T = R + 8

6) The only remaining numbers are 4, 10, and 12. T must be the largest of these, so T = 12

7) If T = 12 and T = R + 8, then R must be 4

12 = 4 + 8

8) By process of elimination, P must be 10

9) Now we can calculate P + R – T:

10 + 4 – 12 = 2

Therefore, the answer is b) 2.

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