The speed of a superfast train T1 is 20 more than the speed of another superfast train T2 Both the t...........

Quantitative Aptitude (MTS) Time & distance

The speed of a superfast train T1, is 20% more than the speed of another superfast train . T2 Both the trains start from point N

at the same time and reach point M at the same time. N and M are 500 km apart. T1 stops for 10 minutes on the way to M, but

T2covers the distance without any stops en route. What is the speed of T1 ?

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SSC MTS 22nd July 2022 Shift-1

600 km/h

500 km/h

650 km/h

550 km/h

- Train T1 is 20% faster than Train T2.

- Both trains travel 500 km from point N to point M simultaneously.

- Train T1 stops for 10 minutes during the journey.

- Train T2 does not stop.

Let's identify the correct speed:

- If T2's speed is $ x $ km/h, then T1's speed is $ 1.2x $ km/h.

- Both trains take the same total time, but T1 spends 10 minutes (1/6 hour) more in motion than T2.

- The time formula is $ \text{Distance} = \text{Speed} \times \text{Time} $.

Setup the equation:

$$ \frac{500}{1.2x} + \frac{1}{6} = \frac{500}{x} $$

Solve for $ x $:

- Multiply through by $ 1.2x \cdot x $:

$$ 500x + \frac{1}{6}(1.2x^2) = 500 \cdot 1.2x $$

- Simplify and solve the equation to find $ 1.2x $:

The speed of T1 is 600 km/h.

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