If there are an equal number of parrot and cats in a pet shop and I can only count a total of 102 legs ,then how many animals in total are there in the pet shop.
a.30
b.32
c.34
d.36
Answers
Answer:
There are rabbits and pigeons in a zoo. There are 340 heads and 1,060 legs. How do I find the number of pigeons in the zoo?
All rabbits have 4 legs and pigeons have 2 legs, but both have 1 head
If R denotes rabbit and P denotes pigeons, then the no. of heads are
R + P = 340 (cause both have one head only)
Now equation for no. of legs will be
4R + 2P = 1060 ( rabbits have 4 legs, that's why we multiplied it with 4 and pigeons have 2 legs, that's why multiplied it with 2)
Multiply the 1st equation with ‘2′ and subtract it from 2nd equation
(R + P = 340 )*2
= 2R + 2P = 680
Subtracting it from 2nd equation
4R + 2P - (2R + 2P) = 1060 - 680
= 4R + 2P -2R - 2P = 380
2R = 380
R = 190
Put this in 1st equation
R + P = 380
P = 380 - R = 380
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First of all, we need to know how many legs each animal has. Rabbits have four, and pigeons have two. Rabbits and pigeons both have one head each, so for every head there is, there is one animal. Therefore, we can conclude for sure that there are 340 animals in total.
Now, let r represent rabbits and let p represent pigeons.
Since there are 340 animals in total, we can say r+p=340 .
Now for legs. 4r+2p=1060 . We can simplify this by halving both sides, thus 2r+p=530 .
We have created a system of equations. We can solve for r by subtracting the two equations. We get (2r−r)+(p−p)=(5
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Let us assume all are pigeons in the zoo.
No. of pigeons= 340
Therefore, No. of legs = 680
No. of extra legs = 1060–680 =380
Now rabbit has 4 legs and pigeon has 2 this implies that each rabbit has 2 extra legs than each pigeon.
so, No. of total extra legs/ No. of extra legs per rabbit = 380/2
gives us total number of rabbits in zoo i.e., 190.
And number of pigeons = 340–190= 150.
Thanks.
I don't know how this trick works but I have tried it many times and I found it is very useful because it always give me correct answer,
First of all multiply number of heads with 2 ,
340×2 = 680
Now, subtract the product from number of legs given,
1060–680 = 380
Now, divide the answer by 2, i.e.,
380÷2 = 190
The number you get after division will always represent the animal that have 4 legs.
Now subtract, 190 from total number of animals or total number of heads,
340–190= 150
150 is the number of pigeons and 190 is the number of rabbits.
You can apply this trick in other questions and
(4r+2p=1060)-(r+b=340)
(4r+2p=1060)-2(r+p=340) (Multiply the equation on the right side by 2 in order to simplify the solution)
(4r+2p=1060)-(2r+2p=680)
2r-0p=1060–680
2r=380
2r/2=380/2
r=
190
and,
if p=340-r, then
p=340–190
p=
50
C.H.
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Lets say X are the Rabbits and Y are the pidgeons.
Both have one head so we could make a formula that says:
340 = x + y
Pigeons have 2 legs and rabbits 4 so here is another formula:
1060 = 4x + 2y
Makes sense right?
Now with a bit of thinking we could say this
530 = 2x + y
340 = x + y
If we subtract this we can achieve this:
190 = x , there you have it. There are 190 rabbits.
if we use the first formula that tells us:
340 = 190 + y
therefore: y = 150 , so there are 150 pidgeons.
Let rabbit=r. pigeon=p, r+p=340 & 2r+4p=1060 Simultaneous equation gives
r=150 p=190 Thus rabbit=150 & pigeon=190
let no.of rabits=r ; no.of pigeons=p
each rabit has 1 head and 4 legs
each pigeon has 1 head and 2 legs
from above question we can frame the following two equations
4r+2p=1060 ; r+p=340
solving these two equations
no.of rabits = 190 and no.of pigeons = 150
1060/4 = 265R
340 - 265 = 75
265 - 75 = 190R
190 x 4 = 760 legs
340 - 190 = 150P x 2 = 300 legs
190 Rabbits 150 Pigeons
PS I’m not cleaning up after this mess.
let Rabbit is X and pigeon is Y then we hv
X+Y=340
4X+2Y=1060
And then solve both equations you will get