Speed Time And Distance - Study Mode

[#286] A and B start at the same time with speed of 40 km/hr. and 50 km/hr respectively. If in covering the journey A takes 15 min longer than B, the total distance of the journey is :
Correct Answer

(C) 50 km

Explanation

Solution: $$eqalign{
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{ A }}:{ ext{ B}} cr
& { ext{Ratio of speed = }},4,,:,,5 cr
& { ext{Ratio of time = }},,,,5{ ext{ }}:{ ext{ }}4{ ext{ }} cr
& (5 - 4){ ext{ unit = 15 unit}} cr
& { ext{1 unit = 15 min}} cr
& { ext{So, time taken by B :}} cr
& { ext{ = 4}} imes { ext{15}} cr
& { ext{ = 60 min}} cr
& { ext{ = 1 hr}} cr
& { ext{Distance = S }} imes { ext{ T }} cr
& ,,,,,,,,,,,,,,,,,,,,{ ext{ = 50}} imes { ext{1 }} cr
& ,,,,,,,,,,,,,,,,,,,,{ ext{ = 50 km}} cr} $$

[#287] A man walk a certain distance and rides back in 4 hours 30 minutes. He could ride both ways in 3 hours. The time required by the man to walk both ways is :
Correct Answer

(D) 6 hours

Explanation

Solution: Time taken to ride one way : = $$frac{3}{2}$$ = 1.5 hrs Time taken to walk one way : = 4.5 - 1.5 = 3 hrs Time taken to walk both way : = 3 × 2 = 6 hours

[#288] A man covers a total distance of 100 km on bicycle. For the first 2 hours, the speed was 20 km/hr and for the rest of the journey, it came down to 10 km/hr. The average speed will be :
Correct Answer

(A) $$12frac{1}{2}$$ km/hr

Explanation

Solution: Distance covered in 1 st 2 hr : = 2 × 20 = 40 km Time taken to cover 60 km distance = $$frac{60}{10}$$ = 6 hours $$eqalign{
& { ext{Average speed}} cr
& = frac{{{ ext{Total distance}}}}{{{ ext{Total time}}}} cr
& = frac{{100}}{{2 + 6}} cr
& = frac{{100}}{8} cr
& = 12frac{1}{2}{ ext{ km/hr}} cr} $$

[#289] The diameter of each wheel of car is 70 cm. If each wheel rotates 400 times per minutes, then the speed of the car (in km/hr) if : $$left( {{ ext{Take }}pi = frac{{22}}{7}}
ight)$$
Correct Answer

(C) 52.8 km/hr

Explanation

Solution: Circumference of wheel = 2πr ⇒ 2πr ⇒ 2 × $$frac{22}{7}$$ × $$frac{70}{2}$$ ⇒ 220 cm Speed per hours : = $$frac{{220 imes 400 imes 60}}{{1000 imes 100}}$$ = 52.8 km/hr

[#290] Two men start together to walk a certain distance, one at 4 km/hr and another at 3 km/hr. The former arrives half an hour before the latter. Find the distance :
Correct Answer

(C) 6 km

Explanation

Solution: If the required distance be x km, then $$eqalign{
& frac{x}{3} - frac{x}{4} = frac{1}{2} cr
& Rightarrow frac{{4x - 3x}}{{12}} = frac{1}{2} cr
& Rightarrow frac{x}{{12}} = frac{1}{2} cr
& Rightarrow x = 6,,{ ext{km}} cr} $$