Question

Question 6
6)
In a farm house, there are 55 goats, 80 ducks and 10 sheep with some pigeons, if the
total number of feet be 305 more than the number of heads in the farmhouse, the
number of pigeon is?
​

Answer 1

Answer:

There is 160 pigeon In the farm house

Answer 2

Given,

In a farmhouse:

Number of goats = 55

Number of ducks = 80

Number of sheep = 10

Total number of feet = 305 more than the number of heads in the farmhouse

To find,

The number of pigeons in the farmhouse.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the number of pigeons in the farmhouse is equal to x.

Now, each goat has 4 feet and 1 head each.

So,

The total number of feet of goats

= 4×(total number of goats)

= 4×55 = 220

The total number of heads of goats

= 1×(total number of goats)

= 1×55 = 55

Now, each duck has 2 feet and 1 head each.

So,

The total number of feet of ducks

= 2×(total number of ducks)

= 2×80 = 160

The total number of heads of ducks

= 1×(total number of ducks)

= 1×80 = 80

Now, each sheep has 4 feet and 1 head each.

So,

The total number of feet of sheep

= 4×(total number of sheep)

= 4×10 = 40

The total number of heads of sheep

= 1×(total number of sheep)

= 1×10 = 10

And, each pigeon has 2 feet and 1 head each.

So,

The total number of feet of pigeon

= 2×(total number of pigeons)

= 2×x = 2x

The total number of heads of pigeons

= 1×(total number of pigeons)

= 1×x = x

So, the total number of heads in the farmhouse

= total number of heads of goats + the total number of heads of ducks + the total number of heads of sheep + total number of head of pigeons

= 55 + 80 + 10 + x

= (145+x)

And, the total number of feet in the farmhouse

= total number of feet of goats + the total number of feet of ducks + the total number of feet of sheep + total number of feet of pigeons

= 220 + 160 + 40 + 2x

= (420+2x)

Now, according to the question;

Total number of feet = 305 more than the number of heads in the farmhouse

=> (total number of feet in the farmhouse) = 305 + (total number of heads in the farmhouse)

=> (420+2x) = 305 + (145+x)

=> 420 + 2x = 450 + x

=> x = 30

=> number of pigeons in the farmhouse = 30

Hence, the total number of pigeons in the farmhouse is equal to 30.