Aptitude - Time and Distance - Discussion

@Naveen.

LCM of 21 and 24 is 168,
168/21 = 7,
168/24 = 8.

But the simple way to solve this question is;

Avrg speed = 2xy/x+y,
2 * 21 * 24/ 21+24,
1008/45 = 22.4.

Distance = speed * time,
= 22.4 *10 =224 km/h.

I am not understanding this. Please help me to get this.

The right answer is 234 km.

Average speed = total distance/total time.
Let us assume the total distance = x.
Total time=10 hr
Average speed =2s1 s2 /s1+s2.
s1 = 21km/hr ,s2 = 24km/hr.
2 s1 s2/s1+s2 = x/10.
2 * 21 * 24 = x/10.
x = 224 ans.

I am not getting the answer. If we use another method by finding avg. of speed

ie. 21+24=45/2=22.5x10=225

& even we calculate separately

ie. 5x21 = 105
5x24 = 120
Then 105+120=225

I am confused pls explain

I am not a mathematician. But, a question arises in me that is :

First half of 10 hours = 5 hours.
Second half of 10 hours = 5 hours.

Then, 5 Hours @ 21 KM Per hour = 21x5 = 105 km.
And nest 5 hours @ 24 KM per hour = 24x5 = 120 km.

Total (21x5) + (24x5) = 105 + 120 = 225.

So, why the answer is not 225 KM.

What would be the mistake here?

If there was no mention of first half and 2nd half of 10 hours, (i.e. 10 hours / 2 = 5 hours,) if it was only mentioned that first the person traveled @ 21 KM/hour and then 24 Km/per, then may be it would be solved using any time & distance formula.

Being a ordinary class student, this question has arisen in my mind.

May I kindly be helped with proper answer ?

Average speed = 2xy/x+y.

Here
X =21.
Y = 24.

Then, the average speed is;
2(21)(24)/45 = 22.4.

Average speed= total distance/total time.
22.4 = X/10,
224 = X,
Finally, the distance is 224.

In question, it was mentioned that the first half of the distance so for first half time can not be 5 hrs. For that reason those who are getting 225 will be wrong. If he will travel at 21 km/h ge will not reach half of the distance in 5 hrs.

Since total distance is divided in two equal half part.

Therefor 10 can be written as 5+5 = 10.

Time = Distance/Speed (5 = x/2*21 and next 5 = x/2*24).

Place these value.

x/2*21 + x/2*24 = 10.

By solving x = 224.

Here, They Mentioned half of the journey.

They didn't mention half of the time.