Directions (79-81): Answer the questions based on the information given below.

Seven delivery agents P, Q, R, S, T, U, and V are parked at different spots in a logistics hub. S is 14m west of T, who is 10m west of V. R is east of S. The distance between V and S is twice the distance between R and S. U is 16m north of R. P is 12m east of U. P is 10m north of Q.

What is the shortest distance between R and V?

The correct answer is 12m.

To find the shortest distance between points R and V, we can determine the relative positions and distances of the delivery agents step-by-step along the East-West line.

Step 1: Calculate the total distance between S and V
From the given information:
• S is 14m west of T.
• T is 10m west of V.
Since S, T, and V lie along the same straight East-West line, the distance from S to V is the sum of the distance from S to T and from T to V:

$\text{Distance between S and V}=14\text{m}+10\text{m}=24\text{m}$

Step 2: Determine the position of R relative to S
We are given:
• R is east of S.
• The distance between V and S is twice the distance between R and S.

$\text{Distance between V and S}=2\times \text{Distance between R and S}$

Substituting the distance between S and V (24m) into the formula:

$24\text{m}=2\times \text{Distance between R and S}$

$\text{Distance between R and S}=\frac{24\text{m}}{2}=12\text{m}$

Since R is east of S and lies at a distance of 12m from S, R is located 12m to the east of S along the straight line towards V.

Step 3: Calculate the shortest distance between R and V
Since the total distance between S and V is 24m, and R is 12m east of S:

$\text{Distance between R and V}=\text{Distance between S and V}-\text{Distance between R and S}$

$\text{Distance between R and V}=24\text{m}-12\text{m}=12\text{m}$

Thus, the shortest distance between R and V is 12m.