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The distance between Sahajanpur and Bareilly is of 54 km. A sports car and an electric car leave Sahajanpur for Bareilly simuntaneously. The ratio between the average speed of the sports car and that of the electric car is 5 ∶ 4. The sports car reaches Bareilly and immediately leaves back for Sahajanpur and meets the electric car at Tanda. Find out the distance between Bareilly and Tanda.
1. 6 km
2. 7 km
3. 8 km
4. 5 km

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Correct Answer - Option 1 : 6 km

Given 

Ratio of their speeds = 5 ∶ 4

Dsiatance between Sahajanpur and Bareilly = 54 km

Formula Used 

If a ∶ b ∶ ∶ c ∶ d, then

Product of Extremes = Product of Mean

Calculation 

Speed of a sports car ∶ Speed of an electric car ∶ ∶ 5 ∶ 4

Since, Distance Speed, Distance travelled by sports car ∶ Distance travelled by an electric car ∶ ∶ 5 ∶ 4

Let the distance between Bareilly and Tanda be x km

Then distance travelled by a sports car = 54 + x

While, the distance travelled by an electric car = 54 - x

 ∴ 54 + x ∶ 54 - x ∶ ∶ 5 ∶ 4

On solving this, we get

⇒ 216 + 4x = 270 - 5x

⇒ 9x = 54 

⇒ x = 6 km

∴ The distance between Bareilly and Tanda is of 6 km.

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