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Present Age Ratio

Introduction

Aptitude tests में age ratio problems बहुत common होते हैं। इनमें exact age difference देने की बजाय present ages का ratio दिया जाता है। इस ratio से हम आसानी से equations बनाकर step-by-step solve कर सकते हैं।

ये problems शुरुआत में tricky लग सकती हैं, लेकिन एक clear process follow करने पर ये बहुत आसान हो जाती हैं। आइए इसका logic समझते हैं और एक example solve करते हैं।

Pattern: Present Age Ratio

Pattern

Ratio-based age problems की मुख्य बात:

अगर A और B की ages का ratio x : y है, तो हम लिख सकते हैं:
A = xk, B = yk (जहाँ k एक common multiplier है)

यह multiplier k असली ages के scale को दर्शाता है। Condition का उपयोग करके जैसे ही k मिलता है, दोनों ages तुरंत मिल जाती हैं।

Step-by-Step Example

Question

Rahul और Neha की present ages का ratio 3 : 2 है। उनकी ages में 10 साल का difference है। उनकी present ages ज्ञात करें।

Options:

  1. Rahul 28, Neha 18
  2. Rahul 30, Neha 20
  3. Rahul 32, Neha 22
  4. Rahul 27, Neha 17

Solution

  1. Step 1: Represent the ratio with a multiplier.

    Ratio 3 : 2 है → Rahul = 3k, Neha = 2k.

  2. Step 2: Use the given condition.

    Difference = 10 → (3k - 2k) = k = 10.

  3. Step 3: Find their actual ages.

    Rahul = 3k = 3 × 10 = 30
    Neha = 2k = 2 × 10 = 20

  4. Final Answer:

    Rahul = 30, Neha = 20 → Option B

  5. Quick Check:

    Ratio = 30 : 20 = 3 : 2 ✅
    Difference = 30 - 20 = 10 ✅

Quick Variations

अगर difference की जगह sum of ages दिया हो, तो बस दोनों ages को add करें: 3k + 2k = 5k.

उदाहरण: Ratio 3 : 2 है और sum = 50 → 5k = 50 → k = 10 → Ages = 30 और 20.

Trick to Always Use

  • Step 1: Ages को ratio multiples (xk, yk) की form में लिखें।
  • Step 2: दी गई condition (difference, sum, relation) से k find करें।
  • Step 3: k को वापस substitute करके actual ages निकालें।
  • Step 4: हमेशा ratio check करके verify करें।

Summary

Summary

  • Ages को हमेशा xk और yk के रूप में लिखें ताकि ratio algebra में बदल जाए।
  • Condition (difference, sum या relation) से simple equation बनाकर k find करें।
  • k substitute करके actual ages लिखें और clear रूप में present करें।
  • Ratio और दूसरी condition दोनों को check करके confirm करें।

Example to remember:
Ratio = 3 : 2, Difference = 10 → k = 10 → Ages = 30 & 20.

Practice

(1/5)
1. The ratio of Rahul's age to Neha's age is 3 : 2. The difference between their ages is 10 years. Find their present ages.
easy
A. 30 and 20
B. 20 and 10
C. 15 and 5
D. 25 and 15

Solution

  1. Step 1: Represent the ratio with a multiplier.

    Rahul = 3k, Neha = 2k.

  2. Step 2: Use the difference.

    Difference = 3k - 2k = k = 10 → k = 10.

  3. Step 3: Find actual ages.

    Rahul = 3×10 = 30, Neha = 2×10 = 20.

  4. Final Answer:

    Rahul = 30, Neha = 20 → Option A

  5. Quick Check:

    30 : 20 = 3 : 2 ✅
Hint: Write ages as xk, yk; difference = (x-y)k gives k quickly.
Common Mistakes: Forgetting to use (x-y)k for the difference; mixing up which is larger.
2. The ratio of A to B is 5 : 4. Their total age is 45 years. Find A and B.
easy
A. 25 and 20
B. 20 and 25
C. 30 and 15
D. 15 and 30

Solution

  1. Step 1: Represent ages.

    A = 5k, B = 4k.

  2. Step 2: Use the sum.

    5k + 4k = 9k = 45 → k = 5.

  3. Step 3: Find ages.

    A = 5×5 = 25, B = 4×5 = 20.

  4. Final Answer:

    A = 25, B = 20 → Option A

  5. Quick Check:

    25 : 20 = 5 : 4 ✅
Hint: Sum the ratio parts, divide total by that to get k.
Common Mistakes: Dividing by wrong total parts or swapping A and B in final assignment.
3. Rahul’s age is 30. If the ratio Rahul : Neha is 3 : 2, what is Neha’s age?
easy
A. 15
B. 18
C. 20
D. 25

Solution

  1. Step 1: Express ages as ratio multiples.

    Rahul = 3k, Neha = 2k.

  2. Step 2: Use Rahul's actual age to find k.

    3k = 30 → k = 10.

  3. Step 3: Find Neha's age.

    Neha = 2×10 = 20.

  4. Final Answer:

    Neha = 20 → Option C

  5. Quick Check:

    30 : 20 = 3 : 2 ✅
Hint: If one actual age is given, divide by its ratio part to get k.
Common Mistakes: Using wrong ratio part for the given person (swap if needed).
4. The ratio of P to Q is 4 : 5. If their difference is 6 years, find their ages.
medium
A. 20 and 26
B. 24 and 30
C. 16 and 22
D. 12 and 18

Solution

  1. Step 1: Represent ages.

    P = 4k, Q = 5k.

  2. Step 2: Use the difference.

    5k - 4k = k = 6 → k = 6.

  3. Step 3: Find ages.

    P = 4×6 = 24, Q = 5×6 = 30.

  4. Final Answer:

    P = 24, Q = 30 → Option B

  5. Quick Check:

    30 - 24 = 6 and ratio 24:30 = 4:5 ✅
Hint: Difference = (b-a)k quickly gives k when difference is given.
Common Mistakes: Mixing up which is larger; use larger ratio part for the older person.
5. The ratio of X to Y is 7 : 3 and their total age is 40 years. Find X and Y.
medium
A. 28 and 12
B. 21 and 19
C. 30 and 10
D. 35 and 5

Solution

  1. Step 1: Represent ages.

    X = 7k, Y = 3k.

  2. Step 2: Use the sum.

    7k + 3k = 10k = 40 → k = 4.

  3. Step 3: Find ages.

    X = 7×4 = 28, Y = 3×4 = 12.

  4. Final Answer:

    X = 28, Y = 12 → Option A

  5. Quick Check:

    28 + 12 = 40 and ratio 28:12 = 7:3 ✅
Hint: Total ÷ sum_of_parts = k, then multiply each ratio part by k.
Common Mistakes: Forgetting to multiply both parts by the same k; mixing sum with difference formulas.

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