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IBPS Sample Problems On Allegation

Below are three problems which are based on allegation and you have to solve the arithmetic calculations.

Question 1

In a room, there are some peacocks and some cats. If the total number of eyes in the room is 1246 and the total number of legs is 1406, what is the number of cats in the room?
a)65 b)80 c)54 d)70

Answer : b)80

Solution:

Let X,Y be the number of peacocks and cats respectively.
from observing the given data, the number of heads in the room will be 1246/2 = 623 (since each has two eyes)
i.e X + Y = 623 .....eqn1
peacock has two legs and cat has 4 legs,
2X + 4Y = 1406 .....eqn2.
solving eqn1 and eqn2,
we get Y = 80 and X = 543
Hence the answer is 80.

Question 2

In a forest, there are some monkeys, tigers and parrots.If the total number of heads in the forest is 63 and total number of legs is 166 then find the number of monkeys, if the birds are twice same as the animals.
a)25 b)22 c)26 d)21

Answer : b)22

Solution:

Let X,Y,Z be the number of monkeys, tigers and parrots respectively.
Given that total number of heads is 63 , X+Y+Z=63 ---- eq1
Also total number of legs is 166 , 2X+4Y+2Z = 166 ---- eq2

Birds are twice same as animals,
i.e., 2Z = X+Y => X+Y-2Z=0 ----- eq3
subtracting eq1 from eq3 we get,
3Z=63 => Z = 21.
solving eq1 and eq2 we get,
Y = 20
adding eq2 and eq3 we get,
3X + 5Y = 166 => 3X+5x20 =166 => X=22.
therefore X=22, Y=20 and Z=21
hence the answer is 22.

Question 3

There are some birds, animals and insects in a forest. 4:5, 1:3 are the ratios of birds to animals and animals to insects respectively. If the difference between insects and animals is 250 then find the total number of birds and insects.
a)475 b)200 c)375 d)100

Answer : a)475

Solution:

Part :1
As given that the ratio of animals to insects is 1:3.
Then X, 3X are the number of animals and insects.
now, 3X-1X = 250 (given)
2X = 250
X = 125.
i.e., the number of animals is 125.
and the number of insects is = 3x125 = 375

Part :2
Also given that 4:5 is the ratio of birds and animals
then 5X = 125
=> X = 25.
Therefore the number of birds is 4X = 4x25 = 100
now the total of birds and insects is = 100 + 375 = 475.
Hence the answer is 475.


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