Quantitative Aptitude
Time, Speed and Distance
2,165 Questions
Time, Speed and Distance Questions
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$13$ km/hr
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$20$ km/hr
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$23$ km/hr
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$30$ km/hr
B
Correct answer
Explanation
Let v be the speed of the bicycle. The effective speed with the wind is v + 10 and against the wind is v - 10. The time taken is 60/(v+10) + 60/(v-10) = 8. Solving this quadratic equation: 60(v-10 + v+10) = 8(v^2 - 100), which simplifies to 120v = 8v^2 - 800, or v^2 - 15v - 100 = 0. Factoring gives (v-20)(v+5) = 0, so v = 20 km/hr.
A
Correct answer
Explanation
Let speed be v. 240/v - 240/(v+20) = 2. 120/v - 120/(v+20) = 1. 120(v+20) - 120v = v(v+20). 2400 = v^2 + 20v. v^2 + 20v - 2400 = 0. (v+60)(v-40) = 0. v = 40.
B
Correct answer
Explanation
480/x - 480/(x-20) = -4. 480(x-20 - x) / (x(x-20)) = -4. -9600 / (x^2 - 20x) = -4. x^2 - 20x = 2400. x^2 - 20x - 2400 = 0. (x-60)(x+40) = 0. x = 60.
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Speed of first train $=$ $20$ km/hr , speed of second train $=$ $15$ km/hr
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Speed of first train $=$ $25$ km/hr , speed of second train $=$ $20$ km/hr
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Speed of first train $=$ $15$ km/hr , speed of second train $=$ $10$ km/hr
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Speed of first train $ = $ $30$ km/hr , speed of second train $=$ $25$ km/hr
A
Correct answer
Explanation
Let speed of second train be v. First train is v+5. After 2 hours, distances are 2v and 2(v+5). By Pythagoras, (2v)^2 + (2(v+5))^2 = 50^2. 4v^2 + 4(v^2+10v+25) = 2500. 8v^2 + 40v + 100 = 2500. 8v^2 + 40v - 2400 = 0. v^2 + 5v - 300 = 0. (v+20)(v-15) = 0. v=15. First train = 20, second = 15.
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$100$ km/h
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$200$ km/h
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$300$ km/h
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$400$ km/h
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$2$ hours
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$3$ hours
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$4$ hours
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$5$ hours
D
Correct answer
Explanation
Let speeds be J and j. J + j = 9. Time = 20/J + 20/j = 9. 20(J+j)/(J*j) = 9 => 20(9)/(J*j) = 9 => J*j = 20. Roots of x^2 - 9x + 20 = 0 are 4 and 5. Since John is faster, John = 5, Jude = 4. Time for Jude = 20/4 = 5 hours.
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$300\sqrt {5}m$
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$300 m$
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$300\sqrt {61}m$
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$3000m$
C
Correct answer
Explanation
After 1.5 hours, the north-bound plane travels 1000 * 1.5 = 1500 km, and the west-bound plane travels 1200 * 1.5 = 1800 km. The distance between them is the hypotenuse of a right triangle: sqrt(1500^2 + 1800^2) = sqrt(2250000 + 3240000) = sqrt(5490000) = 300 * sqrt(61) km. The unit in the options is listed as 'm' but should be 'km'.
A
Correct answer
Explanation
200/x - 200/(x+5) = 2. 100/x - 100/(x+5) = 1. 100(x+5-x) = x(x+5). 500 = x^2 + 5x. x^2 + 5x - 500 = 0. (x+25)(x-20) = 0. x = 20.
C
Correct answer
Explanation
Let distance be D. Time = D/3 + D/2 = 5. (2D + 3D) / 6 = 5 => 5D/6 = 5 => D = 6 km.
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$320km$
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$120km$
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$100km$
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$60km$
D
Correct answer
Explanation
The total time is 6 hours 40 minutes, or 20/3 hours. The train's speed is 320 ÷ (20/3) = 48 km/hr. In 1 hour 15 minutes, or 5/4 hours, it covers 48 × 5/4 = 60 km.
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$96 km$
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$98 km$
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$95 km$
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$92 km$
B
Correct answer
Explanation
The truck's speed is 224/4 = 56 kmph. The bike's speed is one-fourth of this, or 14 kmph. In 7 hours, the bike covers 14 x 7 = 98 km.
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$110$ m
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$200$ m
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$100$ m
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$250$ m
C
Correct answer
Explanation
Speed = 36 km/hr = 36 * (5/18) m/s = 10 m/s. Distance = Speed * Time = 10 m/s * 10 s = 100 m.
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$8\ h$
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$4\ h$
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$7\ h$
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$6\ h$
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$1.620$ km
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$1.950$ km
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$1.310$ km
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$1.450$ km
A
Correct answer
Explanation
Speed = 13.5 m/s. Time = 2 minutes = 120 seconds. Distance = Speed * Time = 13.5 * 120 = 1620 meters = 1.620 km.
C
Correct answer
Explanation
Distance = speed * time. Time = 50 minutes = 50/60 hours = 5/6 hours. Distance = 42 * (5/6) = 7 * 5 = 35 km.