Speed Time And Distance - Study Mode

[#351] A and B run a kilometre and A wins by 25 sec. A and C run a kilometre and A wins by 275 m. When B and C run the same distance, B wins by 30 sec. The time taken by A to run a kilometre is :
Correct Answer

(A) 2 min 25 sec

Explanation

Solution: Let the time taken by A to cover 1 km = x sec Time taken by B and C to cover the same distance = (x + 25) sec and (x + 55) sec $$eqalign{
& frac{{ ext{A}}}{{ ext{C}}} = frac{{29}}{{40}} = frac{x}{{x + 55}} cr
& Rightarrow 29x + 1595 = 40x cr
& Rightarrow x = frac{{1595}}{{11}} cr
& Rightarrow x = 145 cr} $$ ∴ Time taken by A = 145 sec = 2 minutes 25 seconds

[#352] A moving train passes a platform 50 m long in 14 seconds and a lamp post in 10 seconds. The speed of the train (in km/hr) is :
Correct Answer

(D) 45 km/hr

Explanation

Solution: Let length of train be x and speed be S S = $$frac{x + 50}{14}$$ , also S = $$frac{x}{10}$$ Then, $$frac{x + 50}{14}$$ = $$frac{x}{10}$$ 5x + 250 = 7x 2x = 250 x = 125 ∴ Speed : = $$frac{125}{10}$$ × $$frac{18}{5}$$ = 45 km/hr

[#353] A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance will be :
Correct Answer

(B) 13 minutes 20 seconds

Explanation

Solution: Speed of the train : = $$frac{10 × 60}{12}$$ = 50 km/hr Now, new speed : = 50 - 5 = 45 km/hr And, required time : = $$frac{10}{45}$$ = $$frac{2}{9}$$ × 60 = 13 minutes 20 seconds

[#354] Each wheel of a car is making 5 revolutions per second. If the diameter of a wheel is 84 cm, then the speed of the car in cm/sec would be :
Correct Answer

(D) 1320 cm/sec

Explanation

Solution: Circumference of the circle = 2πr = 2πr = 2 × $$frac{22}{7}$$ × 42 = 264 cm Distance cover in 1 sec = 264 × 5 = 1320 cm/sec

[#355] P and Q are 27 km away. Two trains with speed of 24 km/hr and 18 km/hr respectively start simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is :
Correct Answer

(B) 81 km

Explanation

Solution: Relative speed = 24 - 18 = 6 km/hr Time required by faster train to overtake slower train : = $$frac{27}{6}$$ = $$4frac{1}{2}$$ hr ∴ Distance between Q and R : = 18 × $$4frac{1}{2}$$ = 81 km