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

Let's solve the problem step by step:

Given:

Letters 𝑃, 𝑄, 𝑅, 𝑆, 𝑇 represent the numbers 4,5,10,12,15.

The relationships

Q−S=2S

T=R+S+3

First, let's solve for 

Q and S:

From 

Q−S=2S

Q=3S

This implies Q is three times S. The numbers given are 4,5,10,12,15. Among these, only 

12 can be S and 15 can be Q since 

15=3×5.

So:

S=5

Q=15

Next, we use the second relationship:

T=R+S+3

Since S=5, we have:  T=R+5+3

T=R+8

Now we need to assign the remaining numbers to T and R:

The remaining numbers are 4,10,12.

If R=4:

T=4+8=12

So, 

R=4 and T=12.

This leaves P to be the remaining number, which is 10.

Now we calculate P+R−T: 

P=10

R=4

T=12

So:

P+R−T=10+4−12=2

The value of P+R−T is 2. 

Thus, the correct answer is option (b): 2

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