Speed Time And Distance - Study Mode

[#301] A thief steals a car at 1.30 pm and drive it off 40 km/hr. The theft is discovered at 2 pm and the owner sets off in another car at 50 km/hr he will catch the thief at :
Correct Answer

(B) 4 pm

Explanation

Solution: Distance covered by thief in (2 pm - 1.30 pm) = $$frac{1}{2}$$ hr at speed of 40 km/hr = 40 × $$frac{1}{2}$$ = 20 kms Their relative speed in same direction : = (50 - 40) km/hr = 10 km/hr According to the question, 20 km, is the distance that has to be covered by owner to catch the thief. $$eqalign{
& { ext{Required time}} = frac{{20{ ext{ km}}}}{{10{ ext{ km/hr}}}} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 2{ ext{ hours}} cr} $$ Therefore, he will over take the thief at : = 2 pm + 2 hr = 4 pm

[#302] In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less then Sameer. Abhay's speed (in km/hr) is :
Correct Answer

(A) 5

Explanation

Solution: In these type of questions go through options to save your valuable time : Option (A) Abhay's speed = 5 km/hr Abhay's time = $$frac{30}{5}$$ = 6 hr Sameer's time = 6 - 2 = 4 hr Abhay's new time : = $$frac{30}{5 × 2}$$ = 3 hr Hence option (A) is correct as it satisfies all the conditions.

[#303] In a 100 metres race, Kamal defeats Bimal by 5 seconds. If the speed of Kamal is 18 kmph, then the speed of Bimal is :
Correct Answer

(C) 14.4 kmph

Explanation

Solution: Time taken by Kamal : $$ = frac{{100}}{{18 imes frac{5}{{18}}}} = 20sec $$ Time taken by Bimal : $$eqalign{
& = 20 + 5 cr
& = 25sec cr} $$ Speed of Bimal : $$eqalign{
& = frac{{100}}{{25}} imes frac{{18}}{5} cr
& = 14.4{ ext{ kmph}} cr} $$

[#304] At an average speed of 80 km/hr Shatabdi Express reaches Ranchi from Kolkata in 7 hrs. Then the distance between Kolkata and Ranchi is :
Correct Answer

(A) 560 km

Explanation

Solution: D = S × T D = 80 × 7 D = 560 km

[#305] Two trains, one 160 m and the other 140 m long are running in opposite directions on parallel tracks, the first at 77 km an hour and the other at 67 km an hour. How long will they take to cross each other ?
Correct Answer

(B) $$7frac{1}{2}$$ sec

Explanation

Solution: $$eqalign{
& {{ ext{V}}_{{ ext{rel}}{ ext{.}}}} = 77 + 67 = 144{ ext{ km/hr}} cr
& { ext{ = 144}} imes frac{5}{{18}}{ ext{ m/sec}} cr
& = 40{ ext{ m/sec}} cr
& herefore { ext{ T}} = frac{{ ext{D}}}{{{{ ext{V}}_{{ ext{rel}}{ ext{.}}}}}} cr
& Rightarrow { ext{T}} = frac{{140 + 160}}{{40}} cr
& Rightarrow { ext{T}} = frac{{300}}{{40}} cr
& Rightarrow { ext{T}} = 7.5sec { ext{or 7}}frac{1}{2},sec cr} $$