Speed Time And Distance - Study Mode

[#216] A is travelling at 72 km per hour on a highway while B is travelling at a speed of 25 mitres per second. What us the difference in their speeds in mitres per second ?
Correct Answer

(D) 5 m/sec

Explanation

Solution: A's speed : = 72 km/hr = $$left( {72 imes frac{5}{{18}}}
ight)$$ xa0m/sec = 20 m/sec B's speed = 25 m/sec Difference : = (25 - 20) m/sec = 5 m/sec

[#217] A train 100 m long is running at the speed of 30 km/hr. The time (in second) in which it passes a man standing near the railway line is :
Correct Answer

(C) 12 seconds

Explanation

Solution: $$eqalign{
& { ext{Speed : }} cr
& = { ext{ }}30{ ext{ }}km/hr cr
& = { ext{ }}30 imes frac{5}{{18}}{ ext{ }}m/sec cr
& = frac{{25}}{3}m/sec cr
& { ext{So, time = }}frac{D}{S} cr
& ,,,,,,,,,,,,,,,,,,,,, = frac{{100}}{{frac{{25}}{3}}} cr
& ,,,,,,,,,,,,,,,,,,,,, = 12 ,, ext{seconds} cr} $$

[#218] A square playground measure 1127.6164 sq.m. If a man walks $$2frac{9}{{20}}$$ m a minute, the time taken by him to walk one round around it is approximately :
Correct Answer

(B) 54.82 minutes

Explanation

Solution: Let side of the square playground is $$x$$ Ans Area : $$eqalign{
& {x^2} = 1127.6164 cr
& x = sqrt {1127.6164} cr
& x = 33.58 cr} $$ Perimeter of playground : $$eqalign{
& = 4x cr
& = 4 imes 33.58 cr
& = 134.32 cr} $$ Time taken to complete 1 round : $$eqalign{
& = frac{{134.32}}{{2frac{9}{{20}}}} cr
& = frac{{134.32}}{{49}} imes 20 cr
& = 54.82,, ext{minutes} cr} $$

[#219] A man travels for 5 hours 15 minutes. If he covers the first half of the journey at 60 km/h and rest at 45 km/h. Find the total distance travelled by him.
Correct Answer

(C) 270 km

Explanation

Solution: Average speed : $$eqalign{
& = frac{{2 imes 60 imes 45}}{{60 + 45}} cr
& = frac{{1080}}{{21}}{ ext{ km/hr}} cr} $$ Time : $$eqalign{
& = 5 + frac{1}{4}{ ext{ hr}} cr
& { ext{ = }}frac{{21}}{4}{ ext{ hr}} cr} $$ Distance travelled : $$eqalign{
& { ext{ = }}frac{{1080}}{{21}} imes frac{{21}}{4} cr
& = 270{ ext{ km}} cr} $$

[#220] A train is 125 m long. If the train takes 30 sec to cross a tree by the railway line, then the speed of the train is :
Correct Answer

(B) 15 km/hr

Explanation

Solution: $$eqalign{
& { ext{Speed : }} cr
& = { ext{ }}frac{D}{T} cr
& = frac{{125}}{{30}}{ ext{m /sec}} cr
& { ext{ = }}frac{{125}}{{30}} imes frac{{18}}{5}{ ext{ km /hr}} cr
& { ext{ = 15 km /hr}} cr} $$