Brain-Teaser 03 | Ratios, Bees & Circle Games | Key To Enjoy Learning Maths

🧠 BRAIN-TEASER 03
Ratios, Bees & Circle Games

🧱 Cement Mortar: Ratio 1:6, total 42 units. How much cement to add to get 2:9?

✅ Answer: 2 units of cement

📖 Explanation: Current cement=6, sand=36. (6+x)/36 = 2/9 → 9(6+x)=72 → 54+9x=72 → 9x=18 → x=2.

🧂 Salt Water: 30:70 ratio, 1kg solution, evaporate 100g water. New ratio?

✅ Answer: 1:2

📖 Explanation: Salt=300g, water=700g. After evaporation water=600g. Ratio=300:600=1:2.

🐝 Bees Swarm: Half to mustard, 3/4 of rest to rose garden, 10 undecided. Total bees?

✅ Answer: 80 bees

📖 Explanation: Total=x. x/2 + (3/4)(x/2) + 10 = x → x/2 + 3x/8 + 10 = x → 4x/8+3x/8+10=x → 7x/8+10=x → 10=x/8 → x=80.

🔄 Circle Handkerchief Game: 15 children. Skip 1 child works. What about skip 2? Skip 3?

✅ Answer: Skip 2 → Not all. Skip 3 → All get it.

📖 Explanation: Every child gets handkerchief iff gcd(N, step)=1. For 15: step3→gcd=3→no; step4→gcd=1→yes.

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