Aptitude - Time and Distance - Discussion

Another method:
let x = original speed.

And y= original time taken.
So 600/x=y--------(1).

Now we know if speed reduces 30 minutes more will be taken.
i.e 30/60 hours.

So,
600/x-200= y+30/60 here 30/60 means 30 minutes.

Now put the value of y as shown in (1),
So equation will be,
600/x-200= 600/x - 30/60.

You will get,
x2-200x-240000=0 here x2 means x square.
(x-600)(x+200) = 0.
X = 600.

That's why
Time =600/600.
=1 hours.

Hope you guys understand

Here A Shortcut method.

Initial speed = 600km/hr = s1.
Final Speed = 600-200 = 400km/hr = s2.

So, (Taking ratio of speed),
s1 : s2 = 600 : 400= 3 : 2.

So, time taken,
t1 : t2 = 2 : 3 (time and speed inversely proportional).

1 part time= 30 min.

So t1= 2*30 = 60 min = 1hr.

@Ravi, 200 is not the avg speed, it says average speed is reduced by 200, not to 200.

Let me explain you ravi.

Actual speed should be(without any modifications)=dist/time=600/x
With modifications increasing 30min= 600/(x+1/2).

Difference of(actual speed - modified speed) = 200km As mentioned in question.

So (600/x)-(600/(x-1/2)) = 200.

It is as simple as it is. Why you guys are making it complicated.

How can you say.

600/x-600/x+(1/2)= 200.

If '200' is the AVERAGE SPEED than the solution should be,

2*(600/x)*(600/x+(1/2))/(600/x + 600/x+(1/2)) = 200.

Average Speed = 2xy/x+y.

Where, x->first speed in km/hr.
y->second speed in km/hr.

Can anybody suggests if my answer is wrong?

@ISHAN. The speed of the car is 70 km/hr.

Solve the following eqquation:
t-1 = 420/x+10 km/hr.

= 420/x - 420/ x + 10 = t-t-1.
= 420 x + 4200- 420 x = t-t-1.
= 4200 = -1.
= 4200 / 60 (mins)= 70 kms/hr.

@Aarman and @Swetha.

(600/x)-(600/(x+1/2)) = 200
=> (600/x)-((600*2)/2x+1)) = 200
=> (600/x)-((1200)/2x+1)) = 200;

==>(600(2x+1)-1200x)/(x(2x+1)) = 200;
==>(1200x+600-1200x)/(2x^2+x) = 200;

==> (600)/(2x^2+x) = 200;
==> 600 = 400x^2+200x;

==> 400x^2+200x-600 = 0;
==> 200(2x^2+x-3) = 0;

==> 2x^2+x-3 = 0;
==> 2x^2+3x-2x-3 = 0;

==> x(2x+3)-1(2x+3) = 0;
==> (2x+3)(x-1) = 0;

So x=-3/2; x=1;

Since time can never be negative, Therefore by leaving the negative sign we get, x=1 hr and x=3/2 hr.

Please solve this equation 600/x-600/x+1/2=200 I can't understand. As it followed a long solution.

Please solve anyone this equation 600/x-600/x+1/2=200 I can't understand.

This type question take more time in competitive exam so we can go through the answer to question.

If we take 1 as answer.

600/x - 600/x+1/2 = 200.

Then we substitute x = 1.