Correct Answer - Option 4 : 27 km/hr

**Given:**

Distance is 648 km.

**Formula Used:**

Speed = Distance/Time

⇒ Time = Distance/Speed

**Calculation:**

Let the Speed of an Express train be E,

And Speed of a Rajdhani train be R.

According to the question,

⇒ 648/E – 648/R = 12 hours ----(I)

And,

⇒ 648/R – 648/2E = 6 hours

Multiplying the above equation by 2, we get

⇒ 1296/R – 648/E = 12 hours ----(II)

Comparing equation (I) and (II), we get

⇒ 648/E – 648/R = 1286/R – 648/E

⇒ 648/E + 648/E = 1286/R + 648/R

⇒ 1,944/R = 1296/E

⇒ R/E = 1,944/1,296 = 3/2

⇒ E = 2R/3

Using the above value in equation (I), we get

⇒ 648/E – 648/R = 12 hours

⇒ 648/(2R/3) – 648/R = 12

⇒ 972/R – 648/R = 12

⇒ 324/R = 12

⇒ R = 324/12 = 27

**∴ Speed of Rajdhani express is 27km/hr.**