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Dividing a Quantity in Given Ratio

Introduction

Many aptitude problems ask you to split a total amount (money, quantity, marks, time) into parts that follow a given ratio. This is a practical and very common skill - learn the steps and you’ll do these quickly.

The basic idea: if the ratio is a : b : c, the total is divided into (a + b + c) parts and each person (or part) gets their share = (their ratio part ÷ total parts) × total amount.

Pattern: Dividing a Quantity in Given Ratio

Pattern

Key formula:

If total = T and ratio = a : b (or a : b : c ...), then share of first = (a ÷ (a + b + ...)) × T, share of second = (b ÷ (a + b + ...)) × T, etc.

Always add ratio parts to get total parts, then use fraction-of-total to compute each share.

Step-by-Step Example

Question

Split ₹1,000 between A and B in the ratio 3 : 2. Find A’s share and B’s share.

Solution

  1. Step 1: Write the total and the ratio parts.

    Total T = 1000. Ratio = 3 : 2.

  2. Step 2: Find total parts.

    Sum of ratio parts = 3 + 2 = 5.

  3. Step 3: Compute each share (words → math).

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

  4. Step 4: Final Answer.

    A = ₹600, B = ₹400

  5. Step 5: Quick Check (explicit verification).

    Sum check: 600 + 400 = 1000 → matches total ✅.
    Fraction check: A’s fraction = 600 ÷ 1000 = 0.6 = 3/5; B’s fraction = 400 ÷ 1000 = 0.4 = 2/5 → matches the ratio parts.

Question

Divide 84 litres of juice into three containers in the ratio 2 : 3 : 5. Find the quantity in each container.

Solution

  1. Step 1: Write total and ratio parts.

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

  2. Step 2: Sum the ratio parts.

    Sum = 2 + 3 + 5 = 10 parts.

  3. Step 3: Compute each share (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 (explicit verification).

    Sum check: 16.8 + 25.2 + 42 = 84 → matches total ✅.
    Ratio check using fractions: 16.8/84 = 0.2 = 2/10, 25.2/84 = 0.3 = 3/10, 42/84 = 0.5 = 5/10 → matches ratio parts.

Quick Variations

Unequal units: Convert units first (e.g., kg and g) before dividing. Example: 2 kg : 300 g → convert to grams → 2000 g : 300 g → simplify → 20 : 3.

Ratios with decimals: Multiply ratio terms to remove decimals first, then proceed. Example: 1.5 : 2.5 → multiply by 10 → 15 : 25 → simplify → 3 : 5.

Whole-number requirement: If shares must be integers, ensure total divisible by sum of ratio parts or adjust wording (many exam questions choose totals compatible with the ratio).

Trick to Always Use

  • Step 1: Add all ratio parts to get total parts.
  • Step 2: Each share = (that part ÷ total parts) × Total amount.
  • Step 3: For decimals, do fractional multiplication and then round only if the question allows.
  • Step 4: Always perform the Quick Check (sum and fraction checks) to confirm.

Summary

Summary

To divide a quantity in a given ratio:

  • Step 1: Sum the ratio parts (a + b + ...).
  • Step 2: Compute each share = (part ÷ total parts) × Total.
  • Step 3: Verify by adding shares and checking fractions/decimals.

This method works for money, liquids, marks, time, and many other practical problems.

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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