BRAIN-TEASERS 03

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🧠 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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BRAIN-TEASERS 02

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🧠 BRAIN-TEASER 02
LCM, Measuring Rod & Milk Puzzle

🔢 LCM Puzzle: A boy was asked to find the LCM of 3, 5, 12 and another number. But while calculating, he wrote 21 instead of 12 and yet came with the correct answer. What could be the fourth number?

✅ Answer: 28

📖 Explanation: LCM(3,5,12)=60, LCM(3,5,21)=105. For both to be equal, N must contain 2²×7=28. LCM(3,5,12,28)=LCM(3,5,21,28)=420.

📏 Measuring Rod Puzzle: Five pieces of cloth: 15 m, 21 m, 36 m, 42 m, 48 m. All measurable in whole units. Largest possible rod length?

✅ Answer: 3 metres

📖 Explanation: GCD(15,21,36,42,48) = 3. The rod must divide all lengths exactly.

🥛 Milk Measuring Puzzle: 10L, 7L, 3L cans. No markings. Measure exactly 5 litres.

✅ Answer: Yes, 5 litres can be measured

📖 Method: Fill 9L can, pour to 5L → 4L left. Empty 5L, pour 4L into 5L. Fill 9L again, pour to 5L (needs 1L) → 9L left with 8L. Empty 5L, pour 8L into 5L → 3L left in 9L can. ✅

🔁 Two-digit number puzzle: When added to 27 gives its reverse. Find the numbers.

✅ Answer: 14, 25, 36, 47, 58, 69

📖 Explanation: 10a+b+27=10b+a → 9a-9b=-27 → b=a+3. a=1 to 6 gives the numbers.

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