# To travel 648 km, an Express train takes 12 hours more than of Rajdhani. If however, the speed of the Express train is doubled, it takes 6 hours less

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To travel 648 km, an Express train takes 12 hours more than of Rajdhani. If however, the speed of the Express train is doubled, it takes 6 hours less than Rajdhani. The speed of Rajdhani is:
1. 36 km/hr
2. 18 km/hr
3. 45 km/hr
4. 27 km/hr

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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.