Question

One-fourth of birds of a flock are at a river bank and one-fifth of that flock are in their nest.
Remaining 22 birds are wandering in search of food.
What is the number of birds which are in their nest ?
( answer in 20 mins ) ​

Answer 1

Answer:

8 birds

Step-by-step explanation:

let the total number of birds be x

1/4*x +1/5*x +22=x

22= x- x/4+ x/5

22= 20x-5x-4x/20

22=11x/20

x=22*20/11

x=40

no of birds in the nest=1/5*x =1/5*40 = 8 birds

Answer 2

Answer:

• 8 birds were in their nest.

Step-by-step explanation:

Given that:

• One-fourth of birds of a flock are at river bank.
• One-fifth of the birds of that flock are in their nest.
• Remaining 22 birds of that flock are wandering in search of food.

To Find:

• Number of birds which are in their nest.

Let us assume:

• Total number of birds in the flock be n.

Then,

No. of birds at the river bank = n/4

No. of birds in their nest = n/5

Therefore,

$\sf{\dfrac{n}{4}+\dfrac{n}{5}+22=n}$

Transposing variables to LHS and constants to RHS:

$\sf{\dfrac{n}{4}+\dfrac{n}{5}-n=-22}$

∵ LCM of 4 and 5 is 20.

$\therefore\sf{\dfrac{5n+4n-20n}{20}=-22}\\\\\implies\sf{\dfrac{-11n}{20}=-22}$

Transposing 20 from LHS to RHS and changing its sign:

$\sf{-11n = -22 \times20}$

Multiplying -22 by 20:

$\sf{-11n= -440}$

$\sf{\not\!\!{-}11n=\;\not\!\!{-}440}\\\\\sf{11n = 440}\\\\\sf{n = \dfrac{440}{11}}\\\\\sf{n=40}$

Hence, n = 40

Therefore, there were 40 birds in that flock.

No. of birds that were in their nest = n/5 = 40/5 = 8

∴ 8 birds were in their nest.