Aptitude - Time and Distance - Discussion

Here, How can we say given time in the question is equal to the value obtained after subtraction? Please explain me.

Thanks for explaining the answer @VIJETH BK.

@All.

So many of us are confused in where the hell this (150x/100) came from right.

So, my simple explanation is that see the train is 50% faster than car.

Now, consider car speed is X so the train speed will be (X+ 50% of X) Now calculate the train speed.

And you will get (X + 50X/100) = 150X/100.

Hope this helps.

Someone help me in this by explaining this.

I am not understanding this question. Please explain to me.

Can anyone explain to me, how 12.5/60 9is = 5/24?

75/x * 1.5 = 75/x-12.5 (speed of car * 1.5 = speed pf train).
X= 37.5 time taken (min).
Car speed 75/(37.5/60) as time was in mins.

Case1: For car;
D = TV.
75=TV.

Case2:
75={T+(12.5/60)}*1.5V.
75={(60T+12.5)*V}/40.

Now, compare case 1&2.
You get, T = 12.5/20;
As. D = TV.
75 = 12.5/20*V,
V = 120.

For people who still has confusion with the 150*x/100:

Why don't you remember the LCM formula?.. if speed of car is x then speed of train is more than speed of car by 50% of it. so after we calculate 50% of speed of car, we should not forget to add the result of it to the actual speed of car, i.e-
[50% of x]+x
= [(50/100)*x]+x
= [50x/100]+x... now, this is actually [50x/100]+[x/1] the two denominators '100' and '1' here are 100, and 1 and the LCM of the two is 100. This makes 100 the common denominator. now following the rule of LCM, divide the common denominator by the first actual denominator, i.e 100/100, the result is '1', and now multiply the first numerator by this result '1' that keeps 50x*1 that is the same, so basically the first numerator does not change. now, do the same with the second denominator, multiply this common denominator 100 by the second actual denominator, i.e 100/1, the result is '100', and now multiply the second numerator by this result '100' that makes it 100*x that is 100x.. so after the LCM now it looks like:
(50x+100x)/100.

Now take x as common and comprehend this numerator as-
x(50+100)/100
=x(150)/100
=150x/100
DID U GET THIS NOW? THE TRICK LIES IN THE LCM FORMULA !!

This can again be derived to 3x/2, applying the ratio formula.

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Here is another simpler method.. when we calculate speed of train as 50% more than that of the car, in a lay-man's language it simply means speed of train is more than speed of car by half of car's speed, so instead of 50% of car's speed, we can also do half of car's speed, and if car's speed is 'x', then train's speed is

(x/2)+x, applying the same LCM formula, take 2 as the common denominator and the first numerator remains 'x' and the second numerator becomes '2*x'
= (x+2x)/2, now if u remember, 'x' is equivalent to '1*x', as per basic algebra logic- so,
= 3x/2.

GOT THE SAME ANSWER ??

Let car speed = x*100%.
= x * (100/100) = x kmph. // just for understanding

Train is 50% more than car
So train speed = x*(100+50)/100 = 150x/100 = 3x/2 kmph.

In the second step. Let us consider an example a train can reach the destination without stopping at the stations in 10 mins. So the actual time is 10 mins. If it takes extra 2 mins while stopping at the stations. So 10+2=12 mins.

A car if totally takes 12 mins to reach the destination. Train Time taken by train i.e. 12 mins = Time taken by car i.e. 12 mins //Both takes equal time.

10(actual time)+2(extra time) //train = 12 //car.

12-10 = 2 ---->1

NOW COMPARING 1 with our problem. The Extra time taken for the train is given that is 12.5 mins.
Hence the equation will be:
(time taken by car) - (actual time taken by train) = extra time taken by the train.

75/x -75/(3x/2) = 12.5/60.

Since we don't know the time taken by car. Time = distance/speed. So, 75/x similarly for train as 75/(3x/2).

So 75/x -75/(3x/2) = 12.5/60. By solving get the x.