Question 53: Birds in Their Nest

 

Question:
One-fourth of birds of a flock are at a river bank and one-fifth of that flock are in their nest. The remaining 22 birds are wandering in search of food. What is the number of birds in their nest?

Options: (a) 40 (b) 18 (c) 10 (d) 8

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Step 1: Let’s Assign a Variable

Let the total number of birds in the flock be $x$.

• Birds at river bank = $\frac{1}{4}x$

• Birds in nest = $\frac{1}{5}x$

• Birds wandering = 22

We know that all birds together = birds at river + birds in nest + wandering birds:

$$\frac{1}{4}x + \frac{1}{5}x + 22 = x$$

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Step 2: Solve the Equation

Combine fractions:

$$\frac{1}{4}x + \frac{1}{5}x = \frac{5 + 4}{20}x = \frac{9}{20}x$$

So the equation becomes:

$$\frac{9}{20}x + 22 = x$$

Subtract $\frac{9}{20}x$ from both sides:

$$22 = x - \frac{9}{20}x = \frac{11}{20}x$$

Multiply both sides by 20/11:

$$x = 22 \times \frac{20}{11} = 40$$

✅ Total birds in flock = 40

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Step 3: Find Birds in the Nest

Birds in the nest = $\frac{1}{5}x = \frac{1}{5} \times 40 = 8$

✅ Answer: (d) 8

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Fast Calculation Tips

1. Think in fractions: If multiple fractions are involved, find a common denominator quickly.

2. Check total birds: Make sure the fractions + remaining equals the total.

3. Kid-friendly trick: Imagine 20 birds (LCM of 4 and 5). Scale it up until the leftover matches the problem (like filling cups of candy).

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Analogy for Kids:

Think of 40 birds as 40 candies in a jar.

• Some are at the river (1/4 of candies),

• Some are in the nest (1/5 of candies),

• The rest are being eaten (wandering).

Counting each group step by step makes it easy to know how many are in the nest!