Speed Time And Distance - Study Mode

[#336] A man cycles at the speed of 8 km/hr and reaches office at 11 am and when he cycles at the speed of 12 km/hr, he reaches office at 9 am. At what speed should he cycle so that he reaches his office at 10 am ?
Correct Answer

(A) 9.6 km/hrs

Explanation

Solution: First speed = 8 km/hr Second speed = 12 km/hr Starting time will be same in both conditions. Distance travelled by first speed in 2 hours Time take by second speed to travel distance 16 km $$eqalign{
& { ext{Time}} = frac{{{ ext{Distance }}}}{{{2^{{ ext{nd}}}}{ ext{Speed }} - { ext{ }}{{ ext{1}}^{{ ext{st}}}}{ ext{Speed}}}} cr
& { ext{Time}} = frac{{16}}{{12 - 8}} cr
& { ext{Time}} = 4{ ext{ hrs}} cr} $$ Total time taken by second speed = 4 hrs Total distance = 4 × 12 = 48 km Starting time to travel at second speed : = 9 am - 4 hrs = 5 am Total time taken by third speed to reach the office : = 10 am - 5 am = 5 hrs $$eqalign{
& {{ ext{3}}^{{ ext{rd}}}}{ ext{ Speed}} = frac{{{ ext{Total Distance}}}}{{{ ext{Time}}}} cr
& {{ ext{3}}^{{ ext{rd}}}}{ ext{ Speed}} = frac{{48}}{5} cr
& {{ ext{3}}^{{ ext{rd}}}}{ ext{ Speed}} = 9.6{ ext{ km/hrs}} cr} $$

[#337] A man can cover a certain distance in 3 hours 36 minutes If he walks at the rate of 5 km/hr. If he covers the same distance on cycle at the rate of 24 km/hr, then the time taken by him in minutes is :
Correct Answer

(B) 45 minutes

Explanation

Solution: Total distance covered by man in 3 hours 36 minutes is : $$eqalign{
& = 5 imes 3frac{{36}}{{60}} = 5 imes 3frac{3}{5} cr
& = 5 imes frac{{18}}{5} cr
& = 18{ ext{ km}} cr} $$ 18 km is covered at an speed of 24 km/hr ∴ Time taken is : $$eqalign{
& = frac{{18}}{{24}} cr
& = frac{3}{4} imes 60 cr
& = 45{ ext{ minutes}} cr} $$

[#338] A 120 metres long train is running at a speed of 90 km per hour. It will cross a railway platform 230 m long in ?
Correct Answer

(D) 14 sec

Explanation

Solution: Here, speed of the running train is 90 km/hr And length of the train is = 120 metres We know that, When a train crosses through the platform, it cover the distance equal to the length of platform + length of the train So, the time will taken by the train : $$frac{{{ ext{Length of train}} + { ext{Length of platform}}}}{{{ ext{Speed}}}}$$ $$eqalign{
& = frac{{left( {120 + 230}
ight){ ext{ metres}}}}{{90{ ext{ km/hr}}}} cr
& = frac{{350 imes 18}}{{90 imes 5}} cr
& = 14sec cr} $$

[#339] Two trains 180 metres and 120 metres in length are running towards each other on parallel tracks, one at the rate 65 km/hr and another at 55 km/hr. In how many seconds will they be cross each other from the moment they meet ?
Correct Answer

(B) 9 seconds

Explanation

Solution: Time taken by trains to cross each other in opposite direction $$frac{{{l_1} + {l_2}}}{{{ ext{Relative speed in opposite direction}}}}$$ $$eqalign{
& { ext{ = }}frac{{left( {180 + 120}
ight)}}{{left( {65 + 55}
ight)}} cr
& { ext{ = }}frac{{300}}{{120 imes frac{5}{{18}}}} cr
& { ext{ = 9 seconds}} cr} $$

[#340] A distance is covered by a cyclist at a certain speed. If a jogger covers half of the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is :
Correct Answer

(A) 1 : 4

Explanation

Solution: $$eqalign{
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{Cyclist}},:{ ext{Jogger}} cr
& { ext{Ratio of distance}} o ,,,,,2,,,,,,,:,,,,,,,1 cr
& { ext{Ratio of time}},,,,,,,,, o ,,,,,,1,,,,,,,:,,,,,,,2 cr
& { ext{Ratio of their speed }}left( {{ ext{Jogger}}:{ ext{Cyclist}}}
ight) cr} $$ $$eqalign{
& = frac{1}{2}:frac{2}{1} cr
& = 1:4 cr} $$