Practice GAT Quantitative Reasoning questions with answers and explanations.
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The discriminant is b² - 4ac.
Here it is 4² - 4(1)(1) = 16 - 4 = 12.
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Their closing speed is 20 + 25 = 45 km/h.
Time = 90 ÷ 45 = 2 hours.
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A zero discriminant makes the square-root term in the formula zero.
Both solutions therefore coincide.
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For equal distances, average speed is the harmonic mean 2ab/(a + b).
Thus, 2 × 40 × 60 ÷ 100 = 48 km/h.
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For equal time intervals, average speed is the arithmetic mean.
Thus, (40 + 60)/2 = 50 km/h.
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For opposite directions, relative speeds are added.
Thus, 50 + 70 = 120 km/h.
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For motion in the same direction, relative speed is the difference.
Thus, 80 - 55 = 25 km/h.
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To pass a pole, the train covers its own length.
Speed = 150 ÷ 10 = 15 m/s.
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The train covers its length plus the platform length: 300 meters.
Speed = 300 ÷ 20 = 15 m/s.
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Total distance is 100 + 140 = 240 meters.
Relative speed is 10 + 14 = 24 m/s, so time = 10 seconds.
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Relative speed is 66 km/h = 55/3 m/s.
Length = speed × time = 55/3 × 18 = 330 meters.
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Downstream speed equals still-water speed plus stream speed.
Thus, 12 + 3 = 15 km/h.
