Speed Time And Distance - Study Mode

[#246] Two persons A and B start simultaneously from P and Q respectively. A meets B at a distance of 60m from P. After A reaches Q and B reaches P, they turn around and start walking in opposite direction, now B meets A at a distance of 40m from Q. Find distance between P and Q?
Correct Answer

(C) 140 m

Explanation

Solution: P_____60m___R__Xm____40m____Q
Total distance = 100 + X Initially, A traveled 60m and B traveled (40 + X)m.
Since time is same. So, Speed ∝ Distance. $$frac{{{{ ext{S}}_{ ext{a}}}}}{{{{ ext{S}}_{ ext{b}}}}} = frac{{60}}{{40 + { ext{X}}}}$$ Second time, So, now total distance traveled by A = 100 + X + 40 Total distance traveled by B = 100 + X + 60 + X These will be in the ratio of Speed of A and B Thus, $$frac{{{{ ext{S}}_{ ext{a}}}}}{{{{ ext{S}}_{ ext{b}}}}} = frac{{60}}{{40 + { ext{X}}}} = frac{{100 + { ext{X}} + 40}}{{100 + { ext{X}} + 60 + { ext{X}}}}$$ X = 40 Thus Total distance = 100 + X = 100 + 40 = 140 m

[#247] Rohan, Shikha's boyfriend, had to pick her from her home for a live concert on her 23 rd birthday. The venue of the concert and Shikha's home were in opposite directions from Rohan's office. He got late because of some work at office and realised that if he goes to pick Shikha from her home, which was a 48-minute drive from his office, they would be late for the show by 16 minutes. He asked her to start from her home towards his office in an auto-rickshaw and himself started driving towards her home. Both of them started simultaneously, he picked her as soon as they met and they managed to reach the venue just in time for the concert. If Rohan drives at an average speed of 60 km/hr, find the speed (in km/hr) of the auto-rickshaw.
Correct Answer

(C) 12 km

Explanation

Solution: Let the speed of the rickshaw = S km/h. Let after time T they meet. So, 60t + ST = $$frac{{4 imes 60}}{5}$$ $$left[ {{ ext{Since,}},,48,{ ext{min}} = frac{4}{5},,{ ext{hour}}}
ight]$$ Rohan saves 16 min. by making Shikha move as well. So, she saves 16 min by moving for distance X (Let). 2X = $$frac{{60 imes 16}}{5}$$ X = 8 km Speed of Auto rickshaw = 12 km. $$left( {{ ext{ST}} = 8,{ ext{km,}},,{ ext{T}} = frac{2}{3}}
ight)$$

[#248] A plan left 40 minutes late due to bad whether and order to reach its destination 1600 km away in time, it had increase its speed by 400 kmph from its usual speed. Find the usual speed of the plane?
Correct Answer

(D) 800 km/hour

Explanation

Solution: Let usual speed be X kmph, then new speed will be (x + 400) kmph. Time taken to cover 1600 km with speed X kmph, = $$frac{{1600}}{{ ext{x}}}$$ Time taken to cover 1600 km with Speed (x + 400) kmph, = $$frac{{1600}}{{{ ext{x}} + 400}}$$ Now, Time difference = 40 minutes. $$frac{{1600}}{{ ext{x}}} - frac{{1600}}{{{ ext{x}} + 400}} = frac{{40}}{{60}}$$ xa0 xa0 hours x 2 + 400x - 960000 = 0
On solving, x = -1200, 800 Speed cannot be negative, So usual speed will be 800 km/hour

[#249] A thief seeing a policeman at a distance of 150 metres starts running at 10 kmph and the policeman gives immediate chase at 12 kmph. When the thief is overtaken the thief has traveled a distance of:
Correct Answer

(A) 750 m

Explanation

Solution: P__150m___T______x m (Let)_______Q. Let Policeman caught thief at a distance (x + 150)m. And Thief has traveled x m. Speed of Policeman $$eqalign{
& = 12,,{ ext{kmph}} cr
& = frac{{12 imes 5}}{{18}} cr
& = frac{{60}}{{18}},,{ ext{m/sec}} cr} $$
Speed of thief $$eqalign{
& = 10,,{ ext{km}} cr
& = frac{{10 imes 5}}{{18}} cr
& = frac{{50}}{{18}},,{ ext{m/sec}} cr} $$
In this case time is constant means Policeman covered (x + 150)m in same time thief covered x m. Thus, $$eqalign{
& frac{{{ ext{Speed of the thief}}}}{{{ ext{Speed of Policeman}}}} = frac{x}{{150 + x}} cr
& Rightarrow frac{{50}}{{60}} = frac{x}{{150 + x}} cr
& Rightarrow 7500 + 50x = 60x cr
& Rightarrow 10x = 7500 cr
& Rightarrow x = 750,{ ext{m}} cr} $$ So, Thief has traveled 750 m before the caught.

[#250] The ratio between the speed of a bus and train is 15 : 27 respectively. Also, a car covered a distance of 720 km in 9 hours. The speed of the Bus is three-fourth the speed of the car. How much distance will the train cover in 7 hours?
Correct Answer

(B) 756 km

Explanation

Solution: Ratio of speed of Bus and Train = 15 : 27 Let speed of the bus is 15X and Speed of the Train is 27X Car Covered 720 km in 9 hours. So, Speed of the Car = $$frac{{720}}{9}$$xa0 = 80 kmph Given, Speed of the bus is $$frac{3}{4}$$ of Car, So speed of the Bus, = $$frac{{80 imes 3}}{4}$$ xa0 = 60 kmph Thus, 15X = 60 X = 4 So, Speed of the train = 27X = 27 × 4 = 108 kmph. Hence, Train will cover distance in 7 hours, = 108 × 7 = 756 km