# Aptitude - Simplification - Discussion

### Discussion :: Simplification - General Questions (Q.No.13)

13.

A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:

 [A]. 22 [B]. 23 [C]. 24 [D]. 26

Explanation:

Let the number of hens be x and the number of cows be y.

Then, x + y = 48 .... (i)

and 2x + 4y = 140 x + 2y = 70 .... (ii)

Solving (i) and (ii) we get: x = 26, y = 22. The required answer = 26.

 Jyothi said: (Feb 16, 2011) Any short cut?

 Srinu said: (Dec 4, 2011) Can anyone tell me, how 2x and 4y are comming?

 Deepi said: (Feb 1, 2012) Hens have 2 legs and cows have 4 legs. So in-order to calculate number of hens and cows take as 2x+4y.

 Sarthak said: (Jul 26, 2013) Why haven't they count the head and feet of the man? It should be:- 1+x+y = 48. x+y = 47 ---- (1). And 2+2x+4y = 140. => 2x+4y = 138 ---- (2). By solving no.of hens (x) is 25.

 Sk.Gopinath Siva said: (Jul 30, 2013) They asked only for number of hens?

 Dhanalakshmi said: (Aug 27, 2013) How x=26 and y=22 are coming?

 Kaushlendra Singh said: (Dec 30, 2013) Let no.of hens = x. So no.of cows = 48-x. Therefore, 2x + 4*(48-x) = 140. => -2x = 140 - 192. => -2x = -52. => x = 26.

 Hrishikesh Pawar said: (Sep 14, 2014) How to simplify 2x+4y = 140?

 Sandip said: (Dec 23, 2014) Why they are taking 2x+4y = 140, and the equation remains that x+2y = 70? Kindly simplify.

 Prasad said: (Feb 19, 2015) Case 1: The number of heads = 48; He has some hens (let hens as x) and cows (let cows as y) so each has head. So we can take it as x+y = 48. Case 2: The number of feet equals to 140. Hen has 2 legs and cows has 4 legs so 140 we can write as, 2x+4y = 140. By solving this we will get result as x = 26; y = 22.

 Shri said: (Jun 7, 2015) How to solve x+y = 48? x+y = 70, to get x = 26 and y=22. Please tell.

 Sravani said: (Jul 12, 2015) @Shri. You have mistaken X+Y = 48.....1. X+2Y = 70.2. Subtract 1 from 2. We get Y = 22. By substituting we get X value 26.

 Pardeshi said: (Aug 8, 2015) Can anybody explain, how came the value of x and y?

 Sireesha said: (Aug 24, 2015) Any simple shortcut for this type of problems. Please give it.

 Laxmi said: (Oct 23, 2015) Please tell me clearly how came 2x and 4y?

 Sheeraz said: (Nov 7, 2015) Please use common sense here not maths. It can be like 48 cows he has it meas 48 cows and there 4 legs. So multiply this 48*4 = 192. In this question there is 140 legs. So, 192-140 = 52. Hens has 2 legs. So 52/2 = 26.

 Goverdhan said: (Mar 24, 2016) Hens have one head x and the cow has one leg y, then total heads are, x + y = 48. Hens have two legs 2x and the cow has four legs 4y, then total legs are, 2x + 4y = 140. Solve both, => 2x + 2y = 96. => 2x + 4y = 140 then 2y = 44. => y = 22 => x = 26 x is the number of hens, x = 26.

 Franci said: (Mar 29, 2016) Super, thanks for your explanation.

 Gaurav said: (Apr 13, 2016) Here we can see all have 2 legs. So 48 * 2 = 96 have 2 legs, now 140 - 96 = 44 legs still remaining that means some of those we have counted previously have 2 more legs. So, 44/2 = 22 have 4 legs and see that rest 48 - 22 = 26 have 2 legs only.

 Ajay said: (Sep 21, 2016) L/2. 140/2 = 70 70 - 48 = 22=> THIS IS NUMBER OF COWS. AND 48 - 22 = 26 =>THIS IS NUMBER OF HENS.

 Pawan Thapar said: (Oct 13, 2016) Hens: 48 * 2 Cows: 48 * 4 By using allegation & mixture rule, The number of hens is 26 and number of cows is 22.

 Zuheb said: (Dec 26, 2016) @Gaurav, Thanks for simplifying it.

 Preethika said: (Dec 28, 2016) Explain the step 2 of the solution.

 Sravanthi said: (Jan 18, 2017) x = hens and y = cows. Total heads (hens and cows) x+y=48.........(1) Total legs = 140 So hens have 2 legs and also cow has 4 legs===2x+4y=140..........(2) Equation 1 and 2 simplifying x + y = 4. 2x+4y = 140 here equation (1) is multiply by 2. So 2x+2y = 96 x + y = 70 x = 26 and y = 22.

 Geetha said: (Apr 5, 2017) Thank you so much for the given answers with the explanation.

 S Pal said: (May 1, 2017) 4 * 48-140/2 = 26.

 Geet said: (Jun 22, 2017) Cows = L-2H/2. =140-2*48/2 =44/2 =22, Hens =48-22=26.

 Neha said: (Jul 17, 2017) Can anyone please tell me how this 140 is coming? I am confused.

 Jony said: (Aug 20, 2017) 140/4=35 cow head. 48-35=13 hens head. 13*2=26 two legs of hens. Here is 26 shortcut.

 Naveen said: (Sep 16, 2017) 140/2=70-48=22, 48-22=26.

 Ashik.K.S said: (Dec 15, 2017) Applying L/2-h. First step : L/2=140/2=70, Second step :L/2-h=70-48=22(no.of cows), Last step:no.of cows=22, Total heads=48, There fore, The no.of hens=48-22=26.

 Prasad Mandati said: (Jan 11, 2018) Number of Cows = (Feet/2) -- Heads. Number of Hens = Total heads --Number of Cows.

 Lakshmi said: (Apr 8, 2018) There are some cows, bulls and hens in a group. One caretaker looks after 15 animals. The number of bulls is twice the number of cows if the number of head is less than the total number of feet is 186, how many caretakers are there? Can anyone solve this?

 Nambi Sreekanth said: (Apr 14, 2018) Please, explain how the x value get as 26?

 Ramandeep Singh said: (Apr 15, 2018) Hi, Use the formula to get the answer. No of 4 feet animals = Foots -(heads*2)/2.

 Rakshnaa said: (Jun 16, 2018) (48-h)4 + 2h = 140. -4h + 2h =140-192, -2h=-52, h = 26.

 Archita Yadav said: (Jul 18, 2018) 140/2 = 70, 70-48 = 22 (number of cows). 48-22 = 26 (number of hens).

 Shubham Yadav said: (Jul 26, 2018) 2 legs of formula= 2H - L/2. Solve = 2 * 48 - 140/2 = 96 - 70 = 26.

 Shivu said: (Aug 19, 2018) Number of legs/2- head= value of 4 legs animals.

 Pushpa said: (Oct 7, 2018) Thanks @Sheeraz.

 Riya said: (Nov 2, 2018) How come 140? Please explain.

 Jai Prakash said: (Jan 14, 2019) Well said, thanks @Shubham Yadav.

 Deekshant Upadhyay said: (Jan 15, 2019) 48*4=192, 192-140=52÷2=26. Cow=26, Hens=22.

 Devan Mavani said: (Jan 28, 2019) Short cut Total legs/2 - total head = total no of 4 legs animal. = 140/2 - 48. = 70 -48 = 22 four legs animal, Total 48. So 26 two legs animal means hens here.

 Afadmin said: (Mar 19, 2019) It can be solved by; Total legs/2 - total head = total no of 4 legs animal. = 140/2 - 48. = 70 - 48 = 22 four legs animal, Total 48. So 26 two legs animal means hens here.

 Ranjan said: (Jul 6, 2019) Thanks all for explaining.

 Pradyumn Yadav said: (Sep 27, 2019) No of feet of hens = 48 * 2 = 96, So no cows legs = 140-96 = 44 No of cows = 44/2 = 22, No of hens = 48-22 = 26.

 Santosh Shindhe said: (Nov 24, 2019) 140/2 = 70-48 = 22. 48-22 = 26. Thanks all.

 Appikuttan said: (Dec 7, 2019) (Leg÷2) - head = 4legged animals.

 Hanock said: (Apr 9, 2020) Can anyone please tell me how this 140 came? Hens 48*2=96. Cows 48*4=192.

 Manpreet Singh said: (Jul 31, 2020) Total no.of head= 48. Total no.of feet = 140. Hen : Cow 2 : 2+2. (Feet) = 48*2 = 96. Then 140 - 96 = 44, And 44÷2 = 22. Divide by 2 means cow's 2 feet are remaining. 22 are cow and 48-22=26 are hens.

 Abhishek Das said: (Sep 21, 2020) Let us consider the hens=x Cows= 48 - x. Hens have 2 feets and cows have 4 feets therefore x*2+(48-x)*4. so,as per question total no feets are 140. now, 2x + 192 - 4x = 140. So, x = 26.

 Dinesh Shah said: (Dec 24, 2020) Easy way of solution. 48 ( All head) *2 = 96 ( Counting only 2 legs for all ) remaining legs are; 140-96=44 (so these legs are cow's legs) Then divide by 2 ( 2 legs are already counted remain 2 for all cow ). 44/2=22 cows then Hen= 48-22 = 26.

 Avnalti said: (Feb 23, 2021) If you number of hens then you have to find the number of legs of cow, based on the given heads. And that subtract from given total legs, what you get that divided by 2 that's number of hens i.e. 4*48 = 192 - 140 = 52/2 = 26 hens are there. If you want a number of cows. 2*48 = 96. 140 - 96 = 44/2 = 22.

 Chhatra Thapa said: (Jul 25, 2021) 140/2 = 70-48. =22 is cow and the rest are hens=26.