Speed Time And Distance - Study Mode

[#231] A train passes two bridges of length 500 metres and 250 metres in 100 seconds and 60 seconds respectively. The length of the train is :
Correct Answer

(A) 125 metres

Explanation

Solution: Let the length of train be $$l$$ metre According to the question, Time = $$frac{{{ ext{Distance}}}}{{{ ext{Speed}}}}$$ ⇒ 100 =$$frac{{{ ext{500 + }}l}}{{{ ext{Speed}}}}$$ ⇒ Speed = $$frac{{500 + l}}{{100}}$$ xa0 xa0..... (i) Again, 60 = $$frac{{{ ext{250 + }}l}}{{{ ext{Speed of Train}}}}$$ Speed = $$frac{{{ ext{250 + }}l}}{{{ ext{60}}}}$$ xa0 xa0..... (ii) Equation (i) and (ii) $$eqalign{
& Rightarrow frac{{500 + l}}{{100}} = frac{{250}}{{60}} cr
& Rightarrow 1500 + 3l = 1250 + 5l cr
& Rightarrow 2l = 250 cr
& herefore { ext{Length of train = 125 metres}} cr} $$

[#232] Two trains start from a certain place on two parallel tracks in the same direction. The speed of the trains are 45 km/hr and 40 km/hr respectively. The distance between the two trains after 45 minutes will be :
Correct Answer

(C) 3.750 km

Explanation

Solution: Relative speed : $$eqalign{
& = left( {40 - 45}
ight) imes frac{5}{{18}} cr
& = frac{{25}}{{18}}{ ext{ m/s}} cr} $$ ∴ Required distance : $$eqalign{
& { ext{ = }}frac{{25}}{{18}} imes 45 imes 60 cr
& = 3750{ ext{ metres or 3}}{ ext{.75 km}} cr} $$

[#233] If a train with a speed of 60 km/hr. crosses a pole in 30 seconds. The length of the train (in metres) is :
Correct Answer

(D) 500 metres

Explanation

Solution: The length of pole is considered as negligible i.e., = 0 i.e., when a train crosses the pole, it covers the distance equal to the length of train So, the time will be taken by the train = 30 sec And speed = 60 km/hr Then the length of the train : = 60 kmh × 30 sec = 60 × $$frac{5}{18}$$ × 30 metres = 10 × $$frac{5}{3}$$ × 30 = 500 metres

[#234] A man travelled a certain distance train at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was :
Correct Answer

(C) 20 km

Explanation

Solution: $$eqalign{
& {{ ext{S}}_{{ ext{average}}}} = frac{{2ab}}{{a + b}} cr
& = frac{{2 imes 25 imes 4}}{{25 + 4}} cr
& = frac{{200}}{{29}}{ ext{ km/hr}} cr
& { ext{Now, 2D = }}frac{{200}}{{29}} imes left( {5 + frac{4}{5}}
ight) cr
& = frac{{200}}{{29}} imes frac{{29}}{5} cr
& = 40{ ext{ km}} cr
& { ext{ = D = 20 km}} cr} $$

[#235] A man travelled a distance of 72 km in 12 hours. He travelled partly on foot at 5 km/hr and partly on bicycle at 10 km/hr. The distance travelled on foot is :
Correct Answer

(B) 48 km

Explanation

Solution: According to the question, 5 units → 12 hr 1 unit → $$frac{12}{5}$$ hr and, 4 units → $$frac{12}{5}$$ × 4 = $$frac{48}{5}$$ Distance travelled on foot : = $$frac{48}{5}$$ × 5 = 48 km