Aptitude - Area - Discussion

@Fijo.

We can use but you have to convert the given time also into seconds, (i.e) 8 mins to 8*60 = 480 sec. Since it is given as 8 mins and 12 km/hr, we are converting them into 12*1000 = 12000 m and 1 hr = 60 mins.

Now the formula to find the distance is Speed = Distance/Time.

Hence Distance = Speed*Time.

D = 12000/60*8 = 200*8 = 1600 m.

Let x be some value.

The ratios given are 3: 2, (i.e) length will be 3 times the 'x' value and the breadth will be 2 times the 'x' value.

The formula for perimeter is 2(l+b).

l = 3*x.
b = 2*x.

(i.e) 2(3x+2x) = 1600 which is already found is already found.

6x+ 4x = 1600.
10x = 1600.
x = 160.

Now substitute value of x in length.

(i.e) 3x = 3*160 = 480 m.

Substitute value of x in breadth.

(i.e) 2x = 2*x = 2*160 = 320.

Therefore we have length and breadth.

Hence area of a rectangle is l*b = 480*360 = 153600 meters is the answer.

12*1000/60 = 200 m/min.

Since 8 min required. To cover whole ground.

200*8 = 1600 m.

But ground is in ratio 3:2. So total 5.

i.e 1600/5 = 320.

Then 320*2 = 640.

320*3 = 960.

So total length of both sides of rectangle is 960.

Then 960/2 = 480 each side.

Width becomes 320.

Area = 480*20 = 153600.

Speed of the cycling is 12 km/hr and we can finish 8 round at the level if speed but here given speed is km/hr.

So we change meter/minute 12* (1000/60) =200 then we find speed of cycling for one round at one minute.

So 200*8 =1600m is the perimeter of the park.

First we found distance = speed*time.

2(l+b) is the formula of perimeter of rectangle.
Which is the distance we found which is 1600.

Using perimeter formula we found l and b.
Then we found area of rectangle using l*b formula.

Total Length of running = (((12/60)*8)*1000) = 1600 m.

Now, 2*(b+h) = 1600.

Hence, b+h = 800.
Or, 2x+3x = 800.
Or, 5x = 800.
Or, x = 160.

From where, b = 2*160 = 320; and h = 480.

Now the area = 320*480 = 153600 Sq.m.

Length =3x and Breadth = 2x.

Distance = 12000/60 = 200 * 8 = 1600,
3x+2x=1600,
5x^2=1600,
x^2=1600/5=320,
x=160.

3x = 3 * 160 = 480 and 2x = 2 * 160 = 320.

Area = (480*320)m^2.
= 153600 m^2.

I did not understand on how perimeter has a relationship with time and its distance. Please can you tell and explain me in detail. So that I can able to transfer my knowledge to my students.

1 km = 1000 m.

Then, distance=speed*time,
Here speed is 12 km/hr.
12 km is converted to 12*1000 m.
Then, 8 mins is converted to 8/60 sec.
So, 12*1000 * 8/60 = 1600 m.

l/b = 3/2.
s = d/t.

12 x 8/60 = 1.6km,
2(l+b) = 1.6
2(3b/2+b) = 16,
2(5b/2) = 1.6,
b = 1.6/5.
b = 0.32
l = 0.48.

lxb = 0.153km2.
a = 0.1536x10^(6),
a = 153600 m2.

instead of using perimeter just take the total distance as 10x coz length 2 times of 3x and breadth 2 times of 2x
add both u will get 10x
and just find x usin s=d/t