Aptitude - Area - Discussion

1. 

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:

[A]. 15360
[B]. 153600
[C]. 30720
[D]. 307200

Answer: Option B

Explanation:

Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60

Let length = 3x metres and breadth = 2x metres.

Then, 2(3x + 2x) = 1600 or x = 160.

Length = 480 m and Breadth = 320 m.

Area = (480 x 320) m2 = 153600 m2.


Tejveer said: (Nov 25, 2010)  
Why you multiply with 2 in 2(3x+2x) =1600 ?

R.Prabhakaran said: (Dec 26, 2010)  
Why multiply 2(3x+2x)=1600 ?

Divya said: (Dec 27, 2010)  
Perimeter formule 2(l+b), so we are using.

Sankar said: (Feb 19, 2011)  
You said perimeter is 2 (l*b) but in above step perimeter we found as 1600m.

How is it possible two perimeter with different ans?

Ashok said: (Mar 7, 2011)  
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

Manjula said: (Mar 16, 2011)  
From where does 12000 and 60 come.

Chandrika said: (Jun 4, 2011)  
Why multipty 2(3x+2x)=1600?

Hema said: (Jul 25, 2011)  
Sankar you are wrong, the formula for perimeter is 2(l+b) =1600.

Then subs the value for l and b which means 2 (3x+2x) =1600.

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

Tapas Sethy said: (Sep 7, 2011)  
How length equal to 480 and breadth equal to 320?

Sathis said: (Sep 15, 2011)  
Hi ashok just explain briefly.

How to apply in s=d/t.

Kavitha said: (Dec 1, 2011)  
It is in the ratio of 3:2 so 160 x 3=480 and 160 x 2=320.

Sandip Mulmule said: (Jan 13, 2012)  
means 3:2
(3*x)+(2*x)=1600
5(2x)=1600/5
2x=320
x=320/2
x=160
.: 3*160=480
.:2*160=320

Aniruddh said: (Feb 28, 2012)  
@manjula: 12000 and 60 are, 12km/hour will be converted into metre...
1km=1000m hence 12km=120000m and hr is converted as sec.1hr is 60 sec

Anji said: (Jun 6, 2012)  
How did you come to know thats it PERIMETER, please tell.

Ismail said: (Jul 7, 2012)  
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.

Abi said: (Jan 4, 2014)  
How length equal to 480 and breadth equal to 320?

Naveen Kumar said: (Feb 25, 2014)  
How did know perimeter?

Sindhu said: (Mar 9, 2014)  
Why you did not convert 8 minutes to seconds?

Naresh said: (Jul 11, 2014)  
160*3 = 480.160*2 = 320; 480*320 = 153600.

Sandip said: (Jul 22, 2014)  
Why multiply x on l & b ; I am not understand tell me my friends.

Basha said: (Sep 1, 2014)  
@Sindhu.

They are converted in minutes into seconds already in below step.

= 12000*8/60.
= 1600.

Sonal said: (Sep 13, 2014)  
Did not understand please explain in details.

D.Sudhakar said: (Sep 24, 2014)  
Why multiply 2(3x+2x)?

Shashi said: (Oct 6, 2014)  
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.

Bhagyashri said: (Oct 26, 2014)  
1hr is converted in to minutes. i.e 1hr = 60min.

1km = 1000m.

12km = 12000m.

12km/hr = 12000/60.

Engr. Md. Easir Arafat said: (Nov 23, 2014)  
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.

Nikhil said: (Dec 10, 2014)  
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.

Phuntsho said: (Aug 3, 2015)  
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.

Fijo Francis said: (Aug 5, 2015)  
Why we are not using 5/18 formula to convert into m/s?

Can any of you please explain me please ?

Kritika said: (Aug 15, 2015)  
Perimeter of the park is actually the distance covered by the cyclist and hence we use the formula of distance, speed and time.

Mahendra Chozhan said: (Dec 23, 2015)  
@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.

Gayu said: (Jun 14, 2016)  
@all.

2(3x + 2y) =1600 is a parameter of the rectangle so it uses here.

Naveen said: (Jul 8, 2016)  
I clearly understand your explanation, which is help full for all. Thank you.

Aruna said: (Jul 29, 2016)  
Many thanks for this great explanation and session.

Satish said: (Nov 8, 2016)  
Anyone, please answer me. If any solution for this question without using any formula, like "perimeter" we are using above.

Mohan said: (Sep 11, 2017)  
Thanks for this explanation.

Naman Jain said: (Dec 19, 2017)  
12 km /hr --> to convert into m/s
12*(1000/(60*60))?

But in answer its 12*(1000/60) how?

Krishnakumar said: (Jan 27, 2018)  
Perimeter of rectangle formula is 2(l+w).

l is lengtg
W is width
12km/ hr.
1km 1000m.
1 hr is 60 s.
So 12*1000/60 m/s.

Asif said: (Oct 6, 2018)  
Perimeter is the sum of all side of object.

Riya said: (Feb 6, 2019)  
Why 8 minutes not converted to seconds. If it is converted to seconds then we should use 480, but here they used 8 to multiply. Why?

Please anyone explain.

Riya said: (Feb 7, 2019)  
Even 1 hour is converted to minutes only not to seconds. Why?

If we are converting km to metres then hours and minutes should be converted to seconds only.

Right?

Hema M said: (Sep 19, 2019)  
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.

Hema M said: (Sep 19, 2019)  
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.

Hema M said: (Sep 19, 2019)  
1 km /hr = 1000/3600 m/s,
= 5/18 m/s.

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