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Time taken by a bus varies as the distance and inversely as the velocity. On the other side velocity varies directly as cube of petrol used for the journey per kilometer and inversely as the number of boxes the bus is carrying in the journey. Bus complete the journey of 100 km in 2 hours and carry 10 boxes for which petrol required is 10 litters. Find how much of petrol will be used for the journey of 50 km in 5 hours with 4 boxes.

Time taken by a bus varies as the distance and inversely as the velocity. On the other side velocity varies directly as cube of petrol used for the journey per kilometer and inversely as the number of boxes the bus is carrying in the journey. Bus complete the journey of 100 km in 2 hours and carry 10 boxes for which petrol required is 10 litters. Find how much of petrol will be used for the journey of 50 km in 5 hours with 4 boxes. Correct Answer (5/8 × 10<sup>7</sup>/50<sup>4</sup>)<sup>1/3</sup>

Let D be the distance, T be the time, N be the number of boxes and X be the required petrol.

Time taken by a bus varies as the distance and inversely as the velocity

⇒ T × D/V

Velocity varies directly as cube of petrol used for the journey per kilometer and inversely as the number of boxes the bus is carrying in the journey

⇒ V × (X/D)3/N

Let constant factor be k.

T = k × D4/X3 × N

Bus complete the journey of 100 km in 2 hours and carry 10 boxes for which petrol required is 10 litters

⇒ 2 = k × (100)4/103 × 10

⇒ 2 = k ×1000000000/1000

⇒ 2 = k × 107

⇒ k = 2/107

The journey of 50 km in 5 hours with 4 boxes.

T = k × D4/X3 × N

⇒ 5 = 2/107 × 504/X3 × 4

⇒ x = (5/8 × 107/504)1/3

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