# Aptitude - Area - Discussion

### Discussion :: Area - General Questions (Q.No.1)

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

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.

 Subrata Mondal said: (Mar 11, 2021) Thank you so much for this explanation and this season is very helpful.

 Apurv said: (Aug 19, 2021) Why taking x in common both length and Breadth. Why can't be we take as length = x and breadth = y? Please anyone explain.