Speed Time And Distance - Study Mode

[#136] Two boats A and B start towards each other from two places, 108 km apart. Speed of the boats A and B in still water are 12 km/h and 15 km/h respectively. If A proceeds down and B up the stream, they will meet after:
Correct Answer

(B) 4 hours

Explanation

Solution: Let the speed of the stream be x kmph and both the boats meet after t hour.
According to the question, (12 + x) × t + (15 - x) × t = 108 Or, 12t + 15t = 108 Or, 27t = 108 ∴ t = $$frac{{108}}{{27}}$$ = 4 hours

[#137] The speed of a motor-boat is that of the current of water as 36:5. The boat goes along with the current in 5 hours 10 minutes. It will come back in:
Correct Answer

(C) 6 hours 50 minutes

Explanation

Solution: Let the speed of the motor boat = 36x kmph and speed of current = 5x kmph. The boat goes along with the current in 5 hours 10 minutes = $$frac{{31}}{6}$$ hour
$$eqalign{
& { ext{Hence, Distance}} cr
& = {frac{{31}}{6}} imes left( {36x + 5x}
ight) cr
& = frac{{41x + 31}}{6},km cr
& { ext{Speed of boat upstream}} cr
& = 36x + 5x = 31x,{ ext{kmph}} cr
& { ext{Hence, time taken to come back}} cr
& = {frac{{ {41x imes {frac{{31}}{6}} } }}{{31x}}} cr
& = frac{{41}}{6},{ ext{hours}} cr
& = 6,{ ext{hours}},,50,{ ext{minutes}} cr} $$

[#138] In a 100m race, Kamal defeats Bimal by 5 seconds. If the speed of Kamal is 18 kmph, then the speed of Bimal is:
Correct Answer

(C) 14.4 kmph

Explanation

Solution: $$eqalign{
& { ext{Time taken by Kamal}} cr
& = frac{{100}}{{ {frac{{18 imes 5}}{{18}}} }} cr
& = 20,{ ext{seconds}} cr
& { ext{Hence, }} cr
& { ext{Time taken by Bimal}} cr
& 20 + 5 = 25,{ ext{seconds}} cr
& { ext{So, Bimal's speed}} cr
& = frac{{100}}{{25}} cr
& = 4 cr
& = frac{{4 imes 18}}{5} cr
& = 14.4,{ ext{kmph}} cr} $$

[#139] In a 1-kilometre race, A can beat B by 30 meters, while in a 500-meter race B can beat C by 25 meters. By how many meters will A beats C in a 100-meter race?
Correct Answer

(A) 7.85

Explanation

Solution: When A runs 100 meters, B runs 970 meters. Hence, when A runs 100 meter, b runs 97 meter. When B runs 500 meter, C runs 475 meter. When B runs 97 meter, C runs, $$frac{{475 imes 97}}{{500}}$$ xa0 = 92.15 meter. Hence, A will beat C by (100 - 92.15) = 7.85 meters.

[#140] A plane left half an hour later than the scheduled time and in order to reach its destination 1500 kilometers away in time, it had to increase its speed by 33.33 percent over its usual speed. Find its increased speed.
Correct Answer

(D) 1000 kmph

Explanation

Solution: By increasing the speed by 33.33%, it would be able to reduce the time taken for traveling by 25%. But since this is able to overcome the time delay of 30 minutes, 30 minutes must be equivalent to 25% of the time originally taken. Hence, the original time must have been 2 hours and the original speed would be 750 kmph. Hence, the new speed would be 1000 kmph.