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.