Speed Time And Distance - Study Mode

[#341] Prasad goes 96 kilometres on a bike at a speed of 16 km/h, 124 kilometres at 31 km/h in a car, and 105 kilometres at 7 km/h in a horse cart. Find his average speed for the entire distance travelled.
Correct Answer

(B) 13 km/h

Explanation

Solution: $$eqalign{
& { ext{Average speed}} = frac{{96 + 124 + 105}}{{frac{{96}}{{16}} + frac{{124}}{{31}} + frac{{105}}{7}}} cr
& = frac{{325}}{{6 + 4 + 15}} cr
& = frac{{325}}{{25}} cr
& = 13{ ext{ kmph}} cr} $$

[#342] Ram starts from point A at 8 a.m. and reaches point B at 2 p.m. on the same day. On the same day, Raju starts from point B at 8 a.m. and reaches point A at 6 p.m. on the same day. Both points A and B are separated by only a straight line track. At what time they both meet?
Correct Answer

(A) 11:45 a.m.

Explanation

Solution: $$overline {{ ext{A}},,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{B}}} $$ Ram takes = 6 hour Raju takes = 10 hour Let distance = 30 km (LCM of 6, 10) Speed of Ram = $$frac{{30}}{6}$$ = 5 km/hr Speed of Raju = $$frac{{30}}{{10}}$$ = 3 km/hr They will met at $$ = frac{{30}}{8} = 3frac{6}{8}$$ $$eqalign{
& = 3frac{3}{4} imes 60 = 3:45,{ ext{am}} cr
& { ext{Time}} = 8 + 3:45 = 11:45{ ext{ am}} cr} $$

[#343] A and B start moving towords each other from places X and Y, respectively, at the same time on the day. The speed of A is 20% more than of B. After meeting on the way, A and B take p hours and $$7frac{1}{5}$$xa0hours, respectively. What is the value of p?
Correct Answer

(B) 5

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{ ext{A}}&{}&{ ext{B}} \
{{ ext{S}} o }&6&:&5
end{array}] $$eqalign{
& frac{{V1}}{{V2}} = sqrt {frac{{T2}}{{T1}}} cr
& frac{6}{5} = sqrt {frac{{frac{{36}}{5}}}{p}} cr
& frac{{36}}{{25}} = frac{{36}}{{5p}} cr
& p = 5 cr} $$

[#344] Length of a train is 330 metres and it is moving at the speed of 72 km/hr. In how much time will it takes cross a platform of length 710 metres?
Correct Answer

(D) 52 seconds

Explanation

Solution: $$eqalign{
& { ext{Time}} = frac{{330 + 710}}{{72 imes frac{5}{{18}}}}{ ext{ Sec}}{ ext{.}} cr
& = frac{{1040}}{{20}}{ ext{ Sec}}{ ext{.}} cr
& = 52{ ext{ Sec}}{ ext{.}} cr} $$

[#345] A train, 150 m long, is running at 90 km/h. How long (in seconds) will it take to clear a platform that is 300 m long?
Correct Answer

(B) 18

Explanation

Solution: $$eqalign{
& 90{ ext{ km/h}} o frac{{90 imes 5}}{{18}} = 25{ ext{ m/s}} cr
& { ext{Time}} = frac{{150 + 300}}{{25}} = 18,{ ext{seconds}} cr} $$