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 1

$\huge\mathbb{\underline{\underline{SOLUTION:-}}}$

$\huge\mathtt{\purple{Given:-}}$

• In the river $\sf \frac{1}{4} birds\:leave\: their\:folk$

• $\sf \frac{1}{5} are\:in\: nest$

$\bf\underline{To\:Find:-}$

we have to find the number of birds in nest

$\sf\underline{\underline{\red{According\:to\: Question:-}}}$

Let the number of total birds be x

$\sf\implies \frac{x}{5} on\:river\\ \\ \sf\implies \frac{x}{4} in\:nest \\ \\ \sf\implies 22\:are \: wandering\:in\:search\:of\:Food$

So the number of total birds =x

$\sf\implies \frac{x}{4}+\frac{x}{5}+22=x\\ \\ \sf\implies \frac{x\times 5+x\times 4+22}{20}\\ \\ \sf\implies \frac{5x+4x+440}{20}=x\\ \\ \sf\implies 9x+440=20\times x\\ \\ \sf\implies 9x+440=20x\\ \\ \sf\implies 440=20x-9x\\ \\ \sf\implies 440=11x\\ \\ \sf\implies x=\cancel{\frac{440}{11}}=40\\ \\ \sf\implies x=40$

• The total number of birds is 40

• Number of birds of river bank

• $\sf \frac{1}{\cancel4}\times \cancel{40}=10\\ \\ \sf\implies 10\:birds\:on\:river\:bank$

• Number if birds in nest

• $\sf \frac{1}{\cancel5}\times \cancel{40}=8\\ \\ \sf\implies 8 \:birds\:in\:nest$

Total birds =40

So

$\boxed{\mathfrak{\purple{the \:number \:of \:birds \:in\: nest =8}}}$

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