BRAIN-TEASERS 09

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🧠 BRAIN-TEASER 09
Shadows, Woodcutter, Age & Averages

🌳 Tree Height Puzzle: Rahul wanted to find the height of a tree in his garden. He checked the ratio of his height to his shadow's length. It was 4:1. He then measured the shadow of the tree. It was 15 feet. What was the height of the tree?

✅ Answer: 60 feet

📐 Step-by-Step Explanation

This is a similar triangles problem. The ratio of height to shadow length is the same for both Rahul and the tree.

Rahul's height : Rahul's shadow = 4 : 1
Tree's height : Tree's shadow = 4 : 1 (same ratio)
Tree's shadow = 15 feet
Therefore, Tree's height = 4 × 15 = 60 feet.

💡 This method was used by ancient mathematicians like Thales to measure the heights of pyramids and tall structures!

🪵 Woodcutter Puzzle

Problem: A woodcutter took 12 minutes to make 3 pieces of a block of wood. How much time would be needed to make 5 such pieces?

⏱️ Answer: 24 minutes

Step-by-step explanation:
To make 3 pieces from a block, the woodcutter makes 2 cuts.
2 cuts take 12 minutes → 1 cut takes 6 minutes.
To make 5 pieces, he needs 4 cuts.
Time = 4 cuts × 6 minutes = 24 minutes.
💡 Important distinction: Number of cuts = Number of pieces - 1. This is a common trick question!

👕 Cloth Shrinkage

Problem: A cloth shrinks 0.5% when washed. What fraction is this?

📐 Answer: 1/200

Step-by-step explanation:
0.5% means 0.5 per hundred = 0.5/100 = 5/1000 = 1/200.
💡 Percent means "per hundred". To convert a percentage to a fraction, divide by 100 and simplify.

👧 Age Puzzle - Smita and Mother

Problem: Smita's mother is 34 years old. Two years from now, mother's age will be 4 times Smita's present age. What is Smita's present age?

🎂 Answer: 9 years

Step-by-step solution:
Mother's age in 2 years = 34 + 2 = 36 years.
This will be 4 times Smita's present age.
Let Smita's present age = x.
4x = 36 → x = 9.
✅ Smita is 9 years old.
Check: In 2 years, mother 36, Smita 11 → 36 is not 4×11? Wait, careful!
The problem says: "Two years from now mother's age will be 4 times Smita's PRESENT age."
So 36 = 4 × (Smita's present age) → Present age = 9. Correct!

📊 Average Score Puzzle

Problem: Maya got 16 out of 25, Madhura got 20. Their average score was 19. How much did Mohsina score?

📝 Answer: 21

Step-by-step solution:
Average of three scores = (Maya + Madhura + Mohsina) ÷ 3 = 19
Total of three scores = 19 × 3 = 57
Maya + Madhura = 16 + 20 = 36
Mohsina's score = 57 - 36 = 21.
💡 Average problems are common in real life - from exam scores to cricket batting averages!

🌟 Why These Puzzles Matter 🌟

• The shadow ratio teaches similar triangles and indirect measurement.
• The woodcutter puzzle reveals the difference between pieces and cuts.
• Percentage to fraction builds number sense.
• Age problems apply algebra to real-life family relationships.
• Averages help interpret data in everyday life.

Mathematics is a tool for understanding our world!

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