Speed Time And Distance - Study Mode
[#111] A is twice fast as B and B is thrice fast as C is. The journey covered by C in $$frac{3}{2}$$ hours will be covered by A is:
Correct Answer
(A) 15 minutes
Explanation
Solution: Let speed of C = X Then Speed of B = 3X Then Speed of A = 6X Ratio of the speed of A and C = 1 : 6 So, Greater the speed less time taken in journey. C’s speed is 6 times less than A So A will take $$frac{1}{6}$$ of the total time taken C to covered same distance. So, Time taken by A $$eqalign{
& = frac{3}{{2 imes 6}} cr
& = frac{1}{4},,{ ext{hours}} cr
& = 15,,{ ext{minutes}} cr} $$
[#112] The area of square park is 25 sq. Km. Time taken to complete a round of the field once, at a speed of 3 kmph is:
Correct Answer
(C) 6 hours 40 minutes
Explanation
Solution: Area of square = side × side= 25 sq. km.
Side = 5 km. perimeter = 4 × 5 = 20 km. Time taken to complete one round with speed 3 kmph, = $$frac{{20}}{3}$$ = 6.66 hours = 6 hour 40 minutes
[#113] The average speed of a train is 20% less on the return journey than on onward journey. The train halts for half an hour at the destination station before starting on the return journey. If the total time taken for the to and fro journey is 23 hours, covering a distance of 1000 km, the speed of the train on the return journey is:
Correct Answer
(C) 40 km/hr
Explanation
Solution: Train was halted for half an hour
So, total time taken in Journey = 23 - $$frac{1}{2}$$ = 22.5 hours
Average speed in Whole Journey = $$frac{{1000}}{{22.5}}$$xa0 = 44.5 km/hr The average speed on return journey is 20% less than onward journey. Therefore, ratio of average speed of onward and return journey, $$eqalign{
& = frac{{100}}{{80}} cr
& = frac{5}{4} cr} $$ Let average speed of onward journey = 5x Average speed on return journey = 4x Average speed on whole journey = $$frac{{5x + 4x}}{2}$$ 44.5 = $$frac{{5x + 4x}}{2}$$ 89 = 9x x = 9.88 Average speed on return = 9.88 × 4 = 39.52 = 40 km/hr (Approx.)
[#114] A person can row a boat d km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream?
Correct Answer
(D) $$frac{{7}}{{2}}$$ hours
Explanation
Solution: Let the speeds of boat and stream was $$s$$ and $$v$$ km/hr respectively
Then, Actual Speed Downstream = $$left(s + v
ight)$$ xa0km/hr
Actual Speed upstream = $$left(s - v
ight)$$ xa0km/hr
According to question, $$eqalign{
& frac{d}{{s + v}} + frac{d}{{s - v}} = 5,{ ext{hr}}{ ext{.}},15,{ ext{min}}{ ext{.}} cr
& Rightarrow frac{d}{{s + v}} + frac{d}{{s - v}} = frac{{21}}{4},.,.....left( 1
ight) cr
& { ext{and}} cr
& frac{{2d}}{{s - v}} = 7 cr
& Rightarrow frac{d}{{s - v}} = frac{7}{2},......left( 2
ight) cr
& { ext{By equation }}left( 1
ight) - left( 2
ight), cr
& frac{d}{{s + v}} = frac{{21}}{4} - frac{7}{2} cr
& Rightarrow frac{d}{{s + v}} = frac{{21 - 14}}{4} cr
& Rightarrow frac{d}{{s + v}} = frac{7}{4} cr
& Rightarrow frac{{2d}}{{s + v}} = frac{7}{2} cr
& cr} $$ Hence, he takes $$frac{{7}}{{2}}$$ hours to row 2d km distance downstream
[#115] If a man runs at 6 kmph from his house, he misses the train at the station by 8 min. If he runs at 10 kmph, he reaches 7 min before the departure of the train. What is the distance of the station from his house? (in Km).
Correct Answer
(D) $$3frac{3}{4}$$ km
Explanation
Solution: Let the distance of the station from the house of the person = x km $$eqalign{
& { ext{Difference}},{ ext{of}},{ ext{time}} cr
& = 8 + 7 cr
& = 15,{ ext{minutes}} cr
& = frac{1}{4},hr cr
& { ext{Since}},, cr
& { ext{Time}} = frac{{{ ext{Distance}}}}{{{ ext{Speed}}}} cr
& herefore frac{x}{6} - frac{x}{{10}} = frac{1}{4} cr
& Rightarrow frac{{10x - 6x}}{{60}} = frac{1}{4} cr
& Rightarrow frac{{2x}}{{30}} = frac{1}{4} cr
& Rightarrow x = frac{{15}}{4} = 3frac{3}{4}km cr} $$