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Speed, Distance, and Time Equations

CMAT 2023 · Quantitative Techniques & Data Interpretation · Medium · Time Speed Distance

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Anil travelled 300 km by bus and 200 km by taxi. For this, it took him 5 hours and 30 minutes. However if he travels 260 km by bus and 240 km by taxi then he takes 6 minutes more. The speed of the bus is ________ km/hour.

  1. A.

    100

  2. B.

    120

  3. C.

    80

  4. D.

    110

Answer

A

Explanation

Let speed of bus be bb and taxi be tt.

  1. 300b+200t=5.5=112\frac{300}{b} + \frac{200}{t} = 5.5 = \frac{11}{2}
  2. 260b+240t=5.6=285\frac{260}{b} + \frac{240}{t} = 5.6 = \frac{28}{5}

Multiply equation (1) by 6: 1800b+1200t=33\frac{1800}{b} + \frac{1200}{t} = 33 Multiply equation (2) by 5: 1300b+1200t=28\frac{1300}{b} + \frac{1200}{t} = 28

Subtracting the two equations: 500b=5⇒b=100 km/hr\frac{500}{b} = 5 \Rightarrow b = 100 \text{ km/hr}.

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