Ratio Basics & Dividing Amounts

🎯 Learning Objective

Simplify ratios and divide any amount in a given ratio a:b:c.

💡 Concept

• Ratio a:b compares two quantities of the SAME unit — it has no unit itself
• Multiplying or dividing both terms by the same number keeps the ratio unchanged (2:3 = 4:6 = 20:30)
• Simplify a ratio by dividing both terms by their HCF
• Dividing N in ratio a:b:c → one part = N/(a+b+c); shares are a, b, c parts
• Ratios need same units first — compare ₹2 to 50 paise as 200:50 = 4:1

🧮 Key Formulas

One part = Total/(a + b + c)

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Share of A = Total × a/(a + b + c)

✏️ Easy Example

Q. Divide ₹1,500 between A and B in the ratio 2:3.

1. Total parts = 2 + 3 = 5
2. One part = 1500/5 = 300
3. A = 600, B = 900

Answer: A = ₹600, B = ₹900

🇮🇳 Real-Life Example

In a 300-run partnership, Kohli and Rahul scored in the ratio 3:2 — so Kohli made 180. Ratios split scoreboards instantly.

📝 Exam-Level Example

Q. Divide ₹7,200 among A, B and C in the ratio 2:3:4.

1. Total parts = 9
2. One part = 7200/9 = 800
3. A = 1600, B = 2400, C = 3200

Answer: A = ₹1,600, B = ₹2,400, C = ₹3,200

📝 Exam-Level Example

Q. Two numbers are in the ratio 5:7 and their sum is 96. Find the numbers.

1. Parts = 12; one part = 96/12 = 8
2. Numbers = 5 × 8 and 7 × 8

Answer: 40 and 56

🪄 Memory Trick

One part = total ÷ sum of ratio terms. Find that single number first — every share is just a multiple of it.

⚠️ Common Mistakes

• ❌ Adding two ratios term by term (2:3 + 1:2 is NOT 3:5)
• ❌ Dividing by the number of people instead of the sum of ratio terms
• ❌ Comparing quantities in different units without converting

🏆 Exam Tips

• ✅ Check your split: all shares must add back to the total
• ✅ Answer options divisible by the ratio terms are your friends in MCQs

📌 Summary

• Ratio = comparison, no units
• Scale both terms equally — ratio unchanged
• One part = total/(sum of terms)
• Shares must add back to the total