Speed Time And Distance - Study Mode

[#306] Raj and Prem walk in opposite direction at the rate 3 km/hr and 2 km per hour respectively. How far will they be from each other after 2 hrs ?
Correct Answer

(B) 10 km

Explanation

Solution: Since Raju and Prem walk in opposite directions. Distance covered per hour = Relative speed × Time = (3 + 2) × 1 = 5 km xa0 [opposite direction] ∴ Distance covered in 2 hours = 5 × 2 = 10 km

[#307] The ratio of lengths of two trains is 5 : 3 and the ratio of their speeds is 6 : 5. The ratio of time taken by them to cross a pole is ?
Correct Answer

(C) 25 : 18

Explanation

Solution: $$eqalign{
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{A}},{ ext{:}},{ ext{B}},,,,,,,{ ext{length}} cr
& { ext{Ratio of A's and }} o 5:3,,,left( {5x:3x}
ight) cr
& { ext{ B's length}} cr
& { ext{Ratio of A's and }} o 6:5,,,left( {6y:5y}
ight) cr
& { ext{ B's speed}} cr} $$ We know that, When a train crosses a pole, i.e., it covers the distance equal to its length Time taken by train A to cross the pole : $$ = frac{{{ ext{Total distance}}}}{{{ ext{Speed}}}} = frac{{5x}}{{6y}}$$ Time taken by train B to cross the pole : $$ = frac{{{ ext{Total distance}}}}{{{ ext{Speed}}}} = frac{{3x}}{{5y}}$$ Ratio of the their time : $$eqalign{
& = { ext{A}}:{ ext{B}} cr
& = frac{{5x}}{{6y}}:frac{{3x}}{{5y}} cr
& = 25:18 cr} $$

[#308] A man is walking at a speed of 10 kmph. After every km, he takes rest for 5 minutes. How much time will he take to cover a distance of 5 km ?
Correct Answer

(B) 50 min

Explanation

Solution: Time taken by man if he did not stop : $$eqalign{
& = frac{{5{ ext{ km}}}}{{10{ ext{ kmph}}}} cr
& = frac{1}{2}{ ext{hr}} cr
& = 30{ ext{ min}} cr} $$ $$x08ecause $$ Man takes rest for 5 minutes on each km Total rest time = 5 × 4 = 20 min Total travelling time : = 30 min + 20 min = 50 min

[#309] How much time does a train 50 m long, moving at 68 km/hr takes to pass another train 75 m long moving at 50 km/hr in the same direction ?
Correct Answer

(D) 25 sec

Explanation

Solution: Total distance covered by the length of both trains : = 50 m + 75 m And, their relative speed in same direction : = 68 - 50 = 18 km/hr $$x08ecause $$ (Speed subtracted in same direction) Then, the time to cross each other will be : $$eqalign{
& = frac{{125{ ext{ m/s}}}}{{18{ ext{ kms}}}} cr
& = frac{{125{ ext{ }} imes { ext{18}}}}{{18 imes 5{ ext{ }}}}{ ext{m/s}} cr
& left{ {x08ecause 1{ ext{ km/hr = }}frac{5}{{18}}{ ext{ m/s}}}
ight} cr
& = 25sec cr} $$

[#310] A man completed a certain journey by a car. If he covered 30% of the distance at the speed of 20 km/hr, 60% of the distance at 40 km/hr and the remaining distance at 10 km/hr, his average speed for the whole journey was :
Correct Answer

(A) 25 km/hr

Explanation

Solution: Let 10% of journey's = 40 km Then, total journey = 400 kms And, $${ ext{Average speed }} = frac{{{ ext{Total distance }}}}{{{ ext{Total time}}}}$$ $$eqalign{
& 30\% { ext{ of journey}} = 400 imes frac{{30}}{{100}} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 120{ ext{ km}} cr
& 60\% { ext{ of journey}} = 400 imes frac{{60}}{{100}} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 240{ ext{ km}} cr
& 10\% { ext{ of journey}} = 400 imes frac{{10}}{{100}} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 40{ ext{ km}} cr
& { ext{Average speed}} = frac{{400}}{{frac{{120}}{{20}} + frac{{240}}{{40}} + frac{{40}}{{10}}}} cr
& { ext{Average speed}} = frac{{400}}{{left( {6 + 6 + 4}
ight)}} cr
& { ext{Average speed}} = frac{{400}}{{16}} cr
& { ext{Average speed}} = 25{ ext{ km/hr}} cr} $$