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Dividing a Quantity in Given Ratio

Introduction

कई aptitude problems में आपको किसी total amount (पैसा, quantity, marks, time) को दिए गए ratio में parts में बाँटना होता है। यह एक practical और बहुत common skill है - steps सीख लो, तो ये सवाल बहुत जल्दी होंगे।

Base idea: अगर ratio a : b : c है, तो total को (a + b + c) parts में बाँटा जाता है और हर व्यक्ति (या part) को मिलता है = (उसका ratio part ÷ total parts) × total amount.

Pattern: Dividing a Quantity in Given Ratio

Pattern

Key formula:

अगर total = T और ratio = a : b (या a : b : c ...), तो पहले का share = (a ÷ (a + b + ...)) × T, दूसरे का share = (b ÷ (a + b + ...)) × T, आदि।

हमेशा ratio parts को add करके total parts निकालें, फिर fraction-of-total से हर share निकालें।

Step-by-Step Example

Question

₹1,000 को A और B में ratio 3 : 2 में बाँटें। A और B का share निकालें।

Solution

  1. Step 1: Total और ratio parts लिखें।

    Total T = 1000. Ratio = 3 : 2.

  2. Step 2: Total parts निकालें।

    Ratio parts का sum = 3 + 2 = 5.

  3. Step 3: Shares निकालें (words → math)।

    A का share = (3 ÷ 5) × 1000 = (3/5) × 1000 = 600. B का share = (2 ÷ 5) × 1000 = (2/5) × 1000 = 400.

  4. Step 4: Final Answer.

    A = ₹600, B = ₹400

  5. Step 5: Quick Check (verification).

    Sum check: 600 + 400 = 1000 → total match हुआ ✅.
    Fraction check: A fraction = 600 ÷ 1000 = 0.6 = 3/5; B fraction = 400 ÷ 1000 = 0.4 = 2/5 → ratio parts match करती हैं।

Question

84 litres juice को तीन containers में ratio 2 : 3 : 5 में बाँटें। हर container की quantity निकालें।

Solution

  1. Step 1: Total और ratio parts लिखें।

    Total T = 84 litres. Ratio = 2 : 3 : 5.

  2. Step 2: Ratio parts जोड़ें।

    Sum = 2 + 3 + 5 = 10 parts.

  3. Step 3: Shares निकालें (words → math)।

    First container = (2/10) × 84 = 0.2 × 84 = 16.8 litres. Second container = (3/10) × 84 = 0.3 × 84 = 25.2 litres. Third container = (5/10) × 84 = 0.5 × 84 = 42 litres.

  4. Step 4: Final Answer.

    16.8 L, 25.2 L, 42 L

  5. Step 5: Quick Check (verification).

    Sum check: 16.8 + 25.2 + 42 = 84 → total match हुआ ✅.
    Ratio check: 16.8/84 = 0.2 = 2/10, 25.2/84 = 0.3 = 3/10, 42/84 = 0.5 = 5/10 → ratio parts से match करता है।

Quick Variations

Unequal units: Units पहले convert करें (जैसे kg और g)। Example: 2 kg : 300 g → grams में convert → 2000 g : 300 g → simplify → 20 : 3.

Ratios with decimals: Decimals हटाने के लिए पहले ratio terms multiply करें, फिर process करें। Example: 1.5 : 2.5 → 10 से multiply → 15 : 25 → simplify → 3 : 5.

Whole-number requirement: अगर shares integers में चाहिए हों, तो total का sum of ratio parts से divisible होना ज़रूरी है (exam questions में normally ऐसा ही total दिया जाता है)।

Trick to Always Use

  • Step 1: Total parts = सभी ratio parts का sum।
  • Step 2: हर share = (उसका part ÷ total parts) × Total amount।
  • Step 3: Decimal cases में fractional multiplication करें और सिर्फ़ तभी round करें जब question allow करे।
  • Step 4: हमेशा Quick Check करें (sum और fraction checks)।

Summary

Summary

किसी quantity को दिए गए ratio में बाँटने का तरीका:

  • Step 1: Ratio parts को जोड़ें (a + b + ...).
  • Step 2: हर share = (part ÷ total parts) × Total.
  • Step 3: Shares को जोड़कर और fractions/decimals check करके verify करें।

यह तरीका money, liquids, marks, time और कई practical problems में काम आता है।

Practice

(1/5)
1. Split ₹1000 between A and B in the ratio 3 : 2. Find A's and B's share.
easy
A. A ₹600, B ₹400
B. A ₹500, B ₹500
C. A ₹700, B ₹300
D. A ₹400, B ₹600

Solution

  1. Step 1: Compute total parts

    Total parts = 3 + 2 = 5.

  2. Step 2: Find value of one part

    Value of 1 part = 1000 ÷ 5 = 200.

  3. Step 3: Multiply to get shares

    A's share = 3 × 200 = ₹600, B's share = 2 × 200 = ₹400.

  4. Final Answer:

    A ₹600, B ₹400 → Option A

  5. Quick Check:

    600 + 400 = 1000 and 600 : 400 = 3 : 2 ✅
Hint: Find one part by dividing total by sum of ratio parts, then multiply.
Common Mistakes: Forgetting to add ratio parts or mixing order of shares.
2. A sum of ₹540 is divided between X and Y in the ratio 5 : 4. What are their shares?
easy
A. X ₹360, Y ₹240
B. X ₹320, Y ₹220
C. X ₹300, Y ₹240
D. X ₹340, Y ₹200

Solution

  1. Step 1: Compute total parts

    Total parts = 5 + 4 = 9.

  2. Step 2: Find value of one part

    Value of 1 part = 540 ÷ 9 = 60.

  3. Step 3: Multiply to get shares

    X's share = 5 × 60 = ₹300, Y's share = 4 × 60 = ₹240.

  4. Final Answer:

    X ₹300, Y ₹240 → Option C

  5. Quick Check:

    300 + 240 = 540 and ratio = 5 : 4 ✅
Hint: Find 1 part then multiply by each ratio term.
Common Mistakes: Using wrong total parts or arithmetic error when dividing.
3. Split 100 minutes among three tasks in the ratio 2 : 3 : 5. How many minutes for each task?
easy
A. 20, 30, 50
B. 18, 32, 50
C. 22, 28, 50
D. 15, 35, 50

Solution

  1. Step 1: Compute total parts

    Total parts = 2 + 3 + 5 = 10.

  2. Step 2: Find value of one part

    Value of 1 part = 100 ÷ 10 = 10 minutes.

  3. Step 3: Multiply to get shares

    Shares = 2×10 = 20, 3×10 = 30, 5×10 = 50 minutes.

  4. Final Answer:

    20 min, 30 min, 50 min → Option A

  5. Quick Check:

    20 + 30 + 50 = 100 and ratio = 2 : 3 : 5 ✅
Hint: Make sure total parts divide the total exactly; otherwise report decimals.
Common Mistakes: Forgetting to convert parts into actual units (minutes/hours).
4. Divide 84 litres of juice into three containers in the ratio 2 : 3 : 5. Find the quantity in each container.
medium
A. 16 L, 24 L, 44 L
B. 16.8 L, 25.2 L, 42 L
C. 18 L, 27 L, 39 L
D. 20 L, 30 L, 34 L

Solution

  1. Step 1: Compute total parts

    Total parts = 2 + 3 + 5 = 10.

  2. Step 2: Find value of one part

    Value of 1 part = 84 ÷ 10 = 8.4 litres.

  3. Step 3: Multiply to get each share

    First = 2 × 8.4 = 16.8 L, Second = 3 × 8.4 = 25.2 L, Third = 5 × 8.4 = 42 L.

  4. Final Answer:

    16.8 L, 25.2 L, 42 L → Option B

  5. Quick Check:

    16.8 + 25.2 + 42 = 84 and ratio = 2 : 3 : 5 ✅
Hint: Convert to parts → (part fraction) × total gives each share.
Common Mistakes: Rounding early; compute part value to needed precision first.
5. A cake is divided among P, Q and R in the ratio 3 : 5 : 4. If the cake has 360 g, find each person's portion.
medium
A. P 90 g, Q 150 g, R 120 g
B. P 100 g, Q 160 g, R 100 g
C. P 80 g, Q 200 g, R 80 g
D. P 120 g, Q 120 g, R 120 g

Solution

  1. Step 1: Compute total parts

    Total parts = 3 + 5 + 4 = 12.

  2. Step 2: Find value of one part

    Value of 1 part = 360 ÷ 12 = 30 g.

  3. Step 3: Multiply to get shares

    P = 3 × 30 = 90 g, Q = 5 × 30 = 150 g, R = 4 × 30 = 120 g.

  4. Final Answer:

    P 90 g, Q 150 g, R 120 g → Option A

  5. Quick Check:

    90 + 150 + 120 = 360 and ratio = 3 : 5 : 4 ✅
Hint: Always compute 1 part accurately then scale.
Common Mistakes: Miscounting total parts or misplacing multipliers.

Mock Test

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