Speed Time And Distance - Study Mode

[#356] Gautam goes office at a speed of 12 kmph and return homes at 10 kmph. His average speed is :
Correct Answer

(C) 10.9 km/hr

Explanation

Solution: Average speed = $$frac{2xy}{x + y}$$ x = 10 km/hr y = 12 km/hr Average speed = $$frac{{2 imes 10 imes 12}}{{left( {10 + 12}
ight)}}$$ ∴ Average speed = 10.9 km/hr

[#357] In a race of 200 metres, B can give a start of 10 metres to A and C can give a start of 20 metres to B. The start that C can give to A, in the same race, is :
Correct Answer

(C) 29 metres

Explanation

Solution: $$eqalign{
& ,,{ ext{A}},,,,,,,,,,,,,,,,,,,,,,,{ ext{B}},,,,,,,,,,,,,,,,,,,,{ ext{C}} cr
& 190,,,,,,,,,,,,,,,,,200 cr
& 180,,,,,,,,,,,,,,,,,200 cr
& ,,{ ext{A}},,,,,,,,,,,,,,,,,,,,,,,{ ext{B}},,,,,,,,,,,,,,,,,,,{ ext{C}} cr
& 171,,,,,,,,,,,,,,,,,180,,,,,,,,,,,,,,,,200 cr} $$ ⇒ C can give a start of 200 - 171 = 29 metres to A

[#358] A car travelling with $$frac{5}{7}$$ of its usual speed covers 42 km in 1 hr 40 min 48 sec. What is the usual speed of the car ?
Correct Answer

(B) 35 km/hr

Explanation

Solution: $$eqalign{
& { ext{Usual speed}},,,,,,,,:,,,,,,,,{ ext{New speed}} cr
& ,,,mathop {,,,,,,, downarrow imes 5}limits_{35{ ext{ km/h}}}^7 ,,,,,,,,,,,,,,,:,,,,,,,,,,,mathop {,,,,,,, downarrow imes 5}limits_{{ ext{25 km/h}}}^5 cr} $$ $$x08ecause $$ Train covers 42 kms in 1 hr, 40 min, 48 sec with the speed of $$frac{5}{7}$$ of its speed. Then its new speed : $$ = frac{{{ ext{Distance }}}}{{{ ext{Time}}}} = frac{{42{ ext{ km}}}}{{frac{{504}}{{300}}{ ext{hr}}}}$$ [left{ x08egin{gathered}
{ ext{1 hr 40 min 48 sec}} hfill \
{ ext{1hr + 40 min + }}frac{{48}}{{60}}{ ext{min}} hfill \
{ ext{1 hr + }}left( {40 + frac{4}{5}}
ight)min hfill \
1{ ext{ hr}} + frac{{204}}{5}min hfill \
left( {1 + frac{{204}}{{5 imes 60}}}
ight){ ext{ hr}} = frac{{504}}{{300}}{ ext{ hr }} hfill \
end{gathered}
ight}] $$eqalign{
& = frac{{42}}{{504}} imes 300{ ext{ km/hr}} cr
& { ext{ = 25 km/hr}} cr
& x08ecause 5{ ext{ units = 25 km/hr}} cr
& ,,,,{ ext{1 unit = 5 km/hr}} cr
& x08ecause { ext{Usual speed = 7 units}} cr
& x08ecause { ext{Usual speed = 7}} imes { ext{5}} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,= 35{ ext{ km/hr}} cr} $$

[#359] The length of a train and that of a platform are equal. If with a speed of 90 km/hr the train crosses the platform in one minute, then the length of the train (in meters) is ?
Correct Answer

(C) 750 meters

Explanation

Solution: $$eqalign{
& {L_t} = {L_P} = l cr
& S = { ext{90 km /hr }} cr
& ,,,,{ ext{ = }}frac{{90 imes 1000}}{{60}}{ ext{ m/min}} cr
& ,,,,, = 1500 ext{ m/min} cr
& Rightarrow l = {L_t} = {L_P} = frac{{1500}}{2} = 750{ ext{ meters}} cr} $$

[#360] The speed $$3frac{1}{3}$$ m/sec when expressed in km/hr becomes :
Correct Answer

(D) 12 km/hr

Explanation

Solution: 1 m/sec = $$frac{18}{5}$$ km/hr $$frac{10}{3}$$ m/sec = $$frac{10}{3}$$ × $$frac{18}{5}$$ = 12 km/hr