A transport drone P of length 540 meters passes over a landing deck in 22 seconds and flies past a stationary signal tower in 18 seconds. The ratio of the speed of drone P to drone Q is 5 : 2, and drone Q passes a vertical indicator pole in 20 seconds. Find the length of the landing deck as a percentage of the length of drone Q.

The correct option is 50%.

Step-by-step Solution:

Step 1: Calculate the speed of drone P ($v_P$)

When drone P passes a stationary signal tower, the distance covered equals its length ($L_P=540\text{m}$).

$v_P=\frac{540}{18}=30\text{m/s}$

Step 2: Calculate the length of the landing deck ($L_{\text{deck}}$)

When drone P passes over the landing deck in 22 seconds, total distance = $L_P+L_{\text{deck}}$.

$540+L_{\text{deck}}=30\times 22$

$540+L_{\text{deck}}=660$

$L_{\text{deck}}=660-540=120\text{meters}$

Step 3: Calculate the speed of drone Q ($v_Q$)

Given the ratio of speeds $v_P:v_Q=5:2$:

$v_Q=30\times \frac{2}{5}=12\text{m/s}$

Step 4: Calculate the length of drone Q ($L_Q$)

Drone Q passes a vertical indicator pole in 20 seconds:

$L_Q=12\times 20=240\text{meters}$

Step 5: Calculate the required percentage

$\text{Percentage}=\left(\frac{L_{\text{deck}}}{L_Q}\right)\times 100=\left(\frac{120}{240}\right)\times 100=50\%$