Speed Time And Distance - Study Mode

[#86] A train covers a distance between two stations A and B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations A and B is :
Correct Answer

(B) 60 km

Explanation

Solution: Let the distance between the stations A and B br x km Time taken = 45 min = $$frac{3}{4}$$ hrs ∴ Original speed : $$eqalign{
& = left( {x imes frac{4}{3}}
ight){ ext{km/hr}} cr
& { ext{ = }}frac{{4x}}{3}{ ext{km/hr}} cr} $$ New speed : $$eqalign{
& = left( {frac{{4x}}{3} - 5}
ight){ ext{km/hr}} cr
& = left( {frac{{4x - 15}}{3}}
ight){ ext{km/hr}} cr
& herefore frac{x}{{left( {frac{{4x - 15}}{3}}
ight)}} = frac{{48}}{{60}} cr
& Rightarrow frac{{3x}}{{4x - 15}} = frac{4}{5} cr
& Rightarrow 15x = 16x - 60 cr
& Rightarrow x = 60 ext{ km} cr} $$

[#87] A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?
Correct Answer

(A) 100 m

Explanation

Solution: Relative speed of the thief and policeman : = (11 - 10) km/hr = 1 km/hr Distance covered in 6 minutes : $$eqalign{
& = left( {frac{1}{{60}} imes 6}
ight){ ext{km}} cr
& = frac{1}{{10}}{ ext{ km}} cr
& = 100{ ext{ m}} cr} $$ ∴ Distance between the thief and policeman : = (200 - 100) m = 100 m

[#88] Buses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes ?
Correct Answer

(C) 5 km/hr

Explanation

Solution: Let the speed of the man be x km/hr Then, Distance covered by the bus in 2 minutes = Distance covered by the man in 8 min $$eqalign{
& Rightarrow 20 imes frac{2}{{60}} = x imes frac{8}{{60}} cr
& Rightarrow x = left( {frac{2}{3} imes frac{{60}}{8}}
ight) cr
& Rightarrow x = 5{ ext{ km/hr}} cr} $$

[#89] An individual is cycling at a speed of 25 km per hour. He catches his predecessor who had started earlier in two hours. What is the speed of his predecessor who had started 3 hours earlier ?
Correct Answer

(C) 10 kmph

Explanation

Solution: The distance covered in two hour,
= 2 × 25 = 50 km Time taken by first individual = (3h + 2h) = 5h Then, the speed of predecessor, = $$frac{{50}}{5}$$ = 10 kmph.

[#90] A 6 cm long cigarette burns up in 15 minutes if no puff is taken.For every puff, it burns three times as fast during the duration of the puff.If the cigarette burns itself in 13 minutes, then how many puffs has the smoker taken if the average puff lasted 3 seconds?
Correct Answer

(C) 20

Explanation

Solution: Let the number of puffs abe, $$3x imes left( {3 imes frac{1}{{150}}}
ight) + left( {13 imes 60 - 3x}
ight) imes frac{1}{{150}} = 6$$ On solving, We get, x = 20 puffs.