Speed Time And Distance - Study Mode

[#176] Two trains 150 m and 120 m long respectively moving from opposite direction cross each other in 10 sec. If the speed of the second train is 43.2 km/hr, then the speed of the first train is :
Correct Answer

(A) 54 km/hr

Explanation

Solution: Let the speed of second train = x km/hr Their relative speed in opposite direction : = (43.2 + x) km/hr According to the question, $$eqalign{
& { ext{Time = }}frac{{{l_1} + {l_2}}}{{{ ext{Speed}}}} cr
& Rightarrow 10sec = frac{{left( {150 + 120}
ight){ ext{m}}}}{{left( {43.2 + x}
ight) imes frac{5}{{18}}{ ext{ m/s}}}} cr
& Rightarrow 10sec = frac{{270 imes 18}}{{left( {43.2 + x}
ight) imes 5}} cr
& Rightarrow 43.2 imes 5 + 5x = 486 cr
& Rightarrow x = frac{{486 - 216}}{5} cr
& Rightarrow x = 54 cr} $$ ∴ Speed of the second train = 54 km/hr

[#177] Two cars are moving with speed v 1 , v 2 towards a crossing along two roads, If their distance from the crossing be 40 metres and 50 metres at an instant of time then they do not collide if their speeds are such that :
Correct Answer

(B) v 1 : v 2 $$ e $$ 4 : 5

Explanation

Solution: The two cars will collide if their speed are in the ratio of the distance to do covered by them Ratio of distance = 40 : 50 = 4 : 5 For the cars not to collide : v 1 : v 2 $$
e $$ 4 : 5

[#178] In a race of one kilometre. A gives B a start of 100 metres and still wins by 20 seconds. But if A gives B a start of 25 seconds, B wins by 50 metres. The time taken by A to run kilometre is :
Correct Answer

(B) $$frac{{500}}{{29}}{ ext{sec}}$$

Explanation

Solution: Let the time taken by A to run 1000 metres = x seconds Time taken by B to sun 900 metres = x + 20 seconds Speed of A and B : $$ = frac{{1000}}{x},frac{{900}}{{x + 20}}$$ xa0 respectively According to the question, $$frac{{950}}{{frac{{1000}}{x}}} - frac{{1000}}{{frac{{900}}{{x + 20}}}} = 25$$ (As B is the winner now) $$eqalign{
& Rightarrow frac{{950x}}{{1000}} - frac{{1000left( {x + 20}
ight)}}{{900}} = 25 cr
& Rightarrow frac{{19x}}{{20}} - frac{{10x + 200}}{9} = 25 cr
& Rightarrow 171x - 200x - 4000 = 25 imes 20 imes 9 cr
& Rightarrow 29x = 500 cr
& Rightarrow x = frac{{500}}{{29}}{ ext{sec}} cr} $$

[#179] The speed of two trains are in the ratio 6 : 7. If the second train runs 364 km in 4 hours, then the speed of first train is :
Correct Answer

(C) 78 km/hr

Explanation

Solution: Given, Ratio of speed of trains = 6 : 7 Second train covers 364 kms in 4 hours Then, its speed = $$frac{364}{4}$$ = 91 km/hr In the question it is given that speed of the second train = 7 units But actual speed = 91 km/hr i.e., 7 units → 91 km 1 unit → 13 km Therefore, Speed of the first train is : = 6R = 6 × 13 = 78 km/hr

[#180] 2 km 5 metres is equal to ?
Correct Answer

(B) 2.005 km

Explanation

Solution: We know, 1 km = 1000 metres ⇒ 2 km 5 metres = 2 km + $$frac{5}{1000}$$xa0 km = 2 km + 0.005 km = 2.005 km