Aptitude - Time and Distance - Discussion

Let the speed of the car be x.

Then 50 percent of x = x/2.

Speed of the train = x + x/2 = 3x/2.

Hi,

S=D/T
D=75, T=?, S=?

We need to find out the Time T, to get the speed S.

Time difference given as 12.5 mins, within 12.5 mins car is able to cover the same distance as train.

If the speed of the car be 100, then the train speed be 150.
It means 12.5 minus = 1/3 km.
12.5=75/3=25.

Therefore in 12.5 mins distance covered is 25km.
Here distance is given in km.

Therefore convert 12.5 minutes to hour i.e., 12.5/60=0.20833.
0.20833 hr = 25 km.
? = 75 km.

By cross multiplication the time taken to reach 75 km is 0.6249.
.
. . s = d/t.
s = 75/0.6249 = 120km.

Hi,

Why 150/100 why not 100/150?

Suppose car speed is 'x' km/hr and speed of train is 50% higher than car speed,

i.e. [ x + 50/100x].

Hence [ x + 0.5x] = 1.5x.

i.e. 150/100x this is speed of car.

And what about that 12.5 min?

Let car complete distance of 75 km in time t with speed v kmhr

Distance = time x velocity

i.e. 75 km = t * v ------ equation 1

Train waste 12.5 min hence time required for train is t-12.5min

Convert 12.5 min in to hour = 12.5 ÷ 60 = 5 / 24.

i.e. time required for train is t- 5/24.

Speed of train is 50% more than car i.e. 3/2 v.

Distance = time x velocity

Now equation for train is 75 = (t - 5/24) (3 / 2 v) ---------- equation 2.

Now equate equations 1 and 2,

t x v = t - ( 5/24) (3/2 v).

After solving this equation we get,

t = 5 /8.

NOW put t= 5/8 value in equation 1 we get V = 120 i. e. Car speed.

Since the Car covered the half distance while train was halting, the speed of car becomes 75/2 * 60/12.5 = 180KM/hr

Now Train is 50% faster than car so train's speed should be 180 + 90 = 270 KM/hr

Hi @Mancy,

OK here the answer for your question,

Ex:1% of 2 = 1/100*2 = 1/50.

10% of 100 = 10/100*100 = 10.

So now come to our problem ok.

Take speed of the car is X ok. (Consider 100).

Train is 50% faster ok so 100+50 = 150;.

So we need find that 150%X which gives 150/100*X.

All the best.

Still I have a one confusion in my mind that why we are taking speed of a train as,

(50% of car+x) instead of 50% more i.e (50%+x).

We need to convert 12.5 min to hours because the options given are in kmph (kilometre per hour).

To convert 12.5 min to hours you divide it by 60.

To make calculation easier 12.5 is converted into 125 by multiplying it by 10. If you multiply numerator with a number, then you also have to multiply denominator by that number.

Hence in this case it will be 12.5*10/60*10 = 125/600 which is actually the same as 12.5/60.

125/600 = 5/24.

12.5/60 = 5/24.