Aptitude - Simplification - Discussion
Discussion Forum : 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:
Answer: Option
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.
Discussion:
67 comments Page 1 of 7.
Sharmila said:
2 years ago
Total headcount = 48
Feet count =140
The equation for Headcount is Hen + Cow = 48
The equation for leg count is 2Hen + 4Cow = 140
Hen has 2 legs so 2Hen and Cow have 4 legs so 4Cow.
Multiply the equation for headcount × 2.
We get 2Hen + 2 Cow = 96.
2Hen +2Cow = 96
2Hen +4Cow =140
(-) (-) (-)
----------------------
-2Cow=-44,
Cow =44/2,
Cow = 22.
Substitute it in Cow +Hen =48,
22+Hen=48,
Hen = 48-22.
Hen = 26 .
So, Cow =22 and Hen =26.
Feet count =140
The equation for Headcount is Hen + Cow = 48
The equation for leg count is 2Hen + 4Cow = 140
Hen has 2 legs so 2Hen and Cow have 4 legs so 4Cow.
Multiply the equation for headcount × 2.
We get 2Hen + 2 Cow = 96.
2Hen +2Cow = 96
2Hen +4Cow =140
(-) (-) (-)
----------------------
-2Cow=-44,
Cow =44/2,
Cow = 22.
Substitute it in Cow +Hen =48,
22+Hen=48,
Hen = 48-22.
Hen = 26 .
So, Cow =22 and Hen =26.
(13)
Prasad said:
1 decade ago
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.
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.
Avnalti said:
4 years ago
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.
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.
SRAVANTHI said:
9 years ago
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.
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.
Goverdhan said:
9 years ago
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.
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.
Lakshmi said:
7 years ago
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?
Can anyone solve this?
Dinesh Shah said:
5 years ago
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.
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.
(1)
Gaurav said:
9 years ago
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.
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.
Sheeraz said:
10 years ago
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.
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.
Manpreet singh said:
5 years ago
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.
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.
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