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Ratio Increase/Decrease Effect

Introduction

Sometimes, aptitude questions do not directly ask for a ratio. Instead, they say that one person’s age, income, marks, or quantity is increased or decreased, and then they give the new ratio. From this, we must find the original values.

These problems test your ability to carefully apply the changes and then use the ratio relation to form an equation.

Pattern: Ratio Increase/Decrease Effect

Pattern

The key idea:

If the ratio changes after an increase or decrease, write both ratios in terms of variables, then apply the given change step to form an equation.

New ratio = (changed numerator) : (changed denominator).

Step-by-Step Example

Question

The ratio of Rahul’s to Neha’s salary is 3 : 4. After Rahul’s salary is increased by ₹600, the ratio becomes 4 : 5. Find their original salaries.

Solution

  1. Step 1: Represent original salaries.

    Rahul’s salary = 3x Neha’s salary = 4x

  2. Step 2: Apply the change condition.

    Rahul’s new salary = 3x + 600 Neha’s salary remains the same = 4x New ratio = 4 : 5 → (3x + 600)/4x = 4/5

  3. Step 3: Use cross multiplication.

    5 × (3x + 600) = 4 × (4x) 15x + 3000 = 16x

  4. Step 4: Solve the equation.

    16x - 15x = 3000 → x = 3000

  5. Step 5: Find the original salaries.

    Rahul = 3x = 3 × 3000 = ₹9000 Neha = 4x = 4 × 3000 = ₹12000

  6. Step 6: Quick Check.

    Original ratio: 9000 : 12000 = 3 : 4 ✅ After increment: (9000 + 600) : 12000 = 9600 : 12000 = 4 : 5 ✅ Matches both conditions.

Quick Variations

If the decrease is mentioned instead of an increase, subtract the amount before applying the ratio condition.

Sometimes, both values change by different amounts. In that case, adjust each term and then apply the new ratio.

If only the new ratio and difference are given, form equations the same way with variables.

Trick to Always Use

  • Step 1: Represent original values with variables (using given ratio).
  • Step 2: Apply the change (add/subtract).
  • Step 3: Write the new ratio in fraction form.
  • Step 4: Cross multiply and solve for the variable.
  • Step 5: Verify with both original and new ratio.

Summary

Summary

In ratio increase/decrease effect problems:

  • Step 1: Express original values with variables.
  • Step 2: Apply increase/decrease to form the new values.
  • Step 3: Write the new ratio equation and solve.
  • Step 4: Verify by substituting back.

With this method, ratio change problems can be solved quickly and accurately.

Practice

(1/5)
1. Rahul and Neha have salaries in the ratio 3 : 4. After Rahul's salary is increased by ₹600, the ratio becomes 4 : 5. Find their original salaries.
medium
A. Rahul ₹9000, Neha ₹12000
B. Rahul ₹3000, Neha ₹4000
C. Rahul ₹4500, Neha ₹6000
D. Rahul ₹6000, Neha ₹8000

Solution

  1. Step 1: Define variables

    Let Rahul = 3x and Neha = 4x.

  2. Step 2: Apply the increase and form the new-ratio equation

    After increase Rahul = 3x + 600, so (3x + 600) : 4x = 4 : 5.

  3. Step 3: Solve the equation for x

    Cross-multiply: 5(3x + 600) = 4(4x) → 15x + 3000 = 16x → x = 3000.

  4. Final Answer:

    Rahul ₹9000, Neha ₹12000 → Option A

  5. Quick Check:

    After increase Rahul = 9600, Neha = 12000 → 9600:12000 = 4:5 ✅
Hint: Express original values as ratio×k, apply change, form the new-ratio equation and solve for k.
Common Mistakes: Forgetting to add/subtract the change before forming the ratio equation or swapping who got increased.
2. A and B are in the ratio 2 : 3. If A is increased by 6, the ratio becomes 3 : 4. Find A and B.
medium
A. A 48, B 72
B. A 30, B 45
C. A 24, B 36
D. A 60, B 90

Solution

  1. Step 1: Define variables

    Let A = 2x and B = 3x.

  2. Step 2: Apply the increase and form the equation

    After increase A = 2x + 6, so (2x + 6) : 3x = 3 : 4.

  3. Step 3: Solve for x

    Cross-multiply: 4(2x + 6) = 3(3x) → 8x + 24 = 9x → x = 24.

  4. Final Answer:

    A = 48, B = 72 → Option A

  5. Quick Check:

    After increase A = 54, B = 72 → 54:72 = 3:4 ✅
Hint: Set original = ratio×k; add/subtract change; cross-multiply to find k.
Common Mistakes: Not converting the final ratio correctly before cross-multiplying.
3. The ages of P and Q are in the ratio 7 : 9. If Q's age is decreased by 6 years, the ratio becomes 7 : 8. Find their present ages.
medium
A. P 21, Q 27
B. P 42, Q 54
C. P 35, Q 45
D. P 56, Q 72

Solution

  1. Step 1: Define variables

    Let P = 7k and Q = 9k.

  2. Step 2: Apply the decrease and form the new-ratio equation

    After decrease Q = 9k - 6, so 7k : (9k - 6) = 7 : 8.

  3. Step 3: Solve for k

    Cross-multiply: 8(7k) = 7(9k - 6) → 56k = 63k - 42 → 7k = 42 → k = 6.

  4. Final Answer:

    P = 42, Q = 54 → Option B

  5. Quick Check:

    After decrease Q = 48 → 42:48 = 7:8 ✅
Hint: Apply the decrease/increase to the correct term and cross-multiply.
Common Mistakes: Applying the change to the wrong person or sign errors when subtracting.
4. Two quantities are in the ratio 5 : 6. If the first is decreased by 5, the ratio becomes 4 : 5. What were the original quantities?
medium
A. 120 and 144
B. 50 and 60
C. 100 and 120
D. 125 and 150

Solution

  1. Step 1: Define variables

    Let the quantities be 5x and 6x.

  2. Step 2: Apply the decrease and form the equation

    After decrease first becomes 5x - 5, so (5x - 5) : 6x = 4 : 5.

  3. Step 3: Solve for x

    Cross-multiply: 5(5x - 5) = 4(6x) → 25x - 25 = 24x → x = 25.

  4. Final Answer:

    125 and 150 → Option D

  5. Quick Check:

    After decrease first = 120 → 120:150 = 4:5 ✅
Hint: Form (a·k ± change) : (b·k ± change) = new_ratio and solve for k.
Common Mistakes: Not applying the decrease/increase to the correct term or sign mistakes.
5. Two numbers are in the ratio 4 : 5. After the first is increased by 12 and the second by 3, the ratio becomes 5 : 6. Find the original numbers.
hard
A. 256 and 320
B. 100 and 125
C. 228 and 285
D. 200 and 250

Solution

  1. Step 1: Define variables

    Let the numbers be 4x and 5x.

  2. Step 2: Apply the respective increases and form the equation

    After changes: 4x + 12 and 5x + 3, so (4x + 12) : (5x + 3) = 5 : 6.

  3. Step 3: Solve for x

    Cross-multiply: 6(4x + 12) = 5(5x + 3) → 24x + 72 = 25x + 15 → x = 57.

  4. Final Answer:

    228 and 285 → Option C

  5. Quick Check:

    After changes 240 and 288 → 240:288 = 5:6 ✅
Hint: Add respective changes first, then form the ratio equation and solve for the multiplier.
Common Mistakes: Forgetting to add/subtract the given amounts before forming the equation.

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