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Quantitative Aptitudeमात्रात्मक योग्यता · अनुपात और समानुपात

Ratio and Proportionअनुपात और समानुपात questions and answersप्रश्न और उत्तर

Ratio questions reward one habit: turn every ratio into multiples of a single unknown, then let one fact (equal savings, a total, a difference) fix that unknown.

  • Unlimitedअसीमित fresh questionsनए प्रश्न
  • Answersउत्तर always one tap awayहमेशा एक टैप दूर
  • 1 subtopicउप-टॉपिक
  • SSC CGL ~2
  • IBPS PO ~1
  • TCS NQT ~1

Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।

How ratio and proportion worksअनुपात और समानुपात को समझिए

A ratio such as 5 : 4 tells you nothing about the actual amounts until one more fact is given. Write the amounts as 5x and 4x and look for that fact.

When two ratios describe different things (incomes and expenses), they need different unknowns, x and y. A condition such as “each saves the same amount” gives the equation that links them.

Always answer what is asked. The same working gives incomes, expenses and savings, and examiners put all three in the options.

Tricks that save timeसमय बचाने वाली ट्रिक्स

All tricks →सभी ट्रिक्स →

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Exam strategyपरीक्षा रणनीतिRarely taughtकम सिखाई जाने वाली

Back-solve from the middle option

Use it when:कब इस्तेमाल करें: The question is easy to check but slow to set up as an equation (ages, mixtures, “find the number”).

  1. Options on this site are in ascending order (as in most printed papers), so start with B or C.
  2. Plug it into the question. Too big? The answer is above it. Too small? Below.
  3. At most two checks find the answer.
Exampleउदाहरण

The father is 3 times his son’s age; in 12 years he will be twice the son’s age. Son’s age? (a) 10 (b) 12 (c) 14 (d) 16

→ Try 12: father 36; in 12 years 48 and 24 → 2 times. Done.

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: Checking a candidate is a few multiplications; with sorted options each check halves the choices, so two checks cover four options.

Limits:सीमाएँ: Not for “cannot be determined” options or questions with several unknowns. Write the equation then.

Mental mathsमानसिक गणित✓ Checked on 8,640 cases✓ 8,640 मामलों पर जाँची गई

Compare two ratios without dividing

Use it when:कब इस्तेमाल करें: DI questions like “in which year was the ratio highest?” or “which is greater, 37/53 or 41/59?”.

  1. a/b > c/d exactly when a × d > b × c (for positive numbers).
  2. For growth rates, compare (new/old) the same way: no percentages needed.
Exampleउदाहरण

37/53 or 41/59?

→ 37 × 59 = 2,183 and 53 × 41 = 2,173, so 37/53 is bigger.

Why it works, and when it failsयह क्यों काम करती है, और कब नहीं

Why:क्यों: Multiplying both sides of a/b > c/d by the positive number b·d keeps the inequality and removes the division.

Limits:सीमाएँ: Positive numbers only; with negative values the direction can flip.

Solved examplesहल किए गए उदाहरण

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

  1. Example 1उदाहरण 1 · Ratio of incomes and expenditures with equal savings · Easyआसान

    The monthly incomes of Ayaan and Lakshmi are in the ratio 8 : 7, and their expenses are in the ratio 5 : 2. If each saves ₹4,750 a month, what is Ayaan’s monthly income?

    1. ₹1,250
    2. ₹5,250
    3. ₹6,000
    4. ₹38,000
    Answer:उत्तर: ₹6,000
    1. 8x − 5y = 7x − 2y ⇒ 1x = 3y ⇒ y = 1x/3.
    2. Substitute in 8x − 5y = 4,750 to get x = 750.
    3. Ayaan’s income = 8 × 750 = ₹6,000.

  2. Example 2उदाहरण 2 · Ratio of incomes and expenditures with equal savings · Mediumमध्यम

    The monthly incomes of Fatima and Harpreet are in the ratio 11 : 7, and their expenses are in the ratio 5 : 1. If each saves ₹2,400 a month, what is Fatima’s monthly income?

    1. ₹2,000
    2. ₹2,800
    3. ₹4,400
    4. ₹26,400
    Answer:उत्तर: ₹4,400
    1. 11x − 5y = 7x − 1y ⇒ 4x = 4y ⇒ y = x.
    2. Substitute in 11x − 5y = 2,400 to get x = 400.
    3. Fatima’s income = 11 × 400 = ₹4,400.

  3. Example 3उदाहरण 3 · Ratio of incomes and expenditures with equal savings · Hardकठिन

    The monthly incomes of Ananya and Aditya are in the ratio 7 : 5, and their expenses are in the ratio 4 : 1. If each saves ₹2,600 a month, what is Aditya’s monthly income?

    1. ₹400
    2. ₹3,000
    3. ₹4,200
    4. ₹13,000
    Answer:उत्तर: ₹3,000
    1. 7x − 4y = 5x − 1y ⇒ 2x = 3y ⇒ y = 2x/3.
    2. Substitute in 7x − 4y = 2,600 to get x = 600.
    3. Aditya’s income = 5 × 600 = ₹3,000.

  4. Example 4उदाहरण 4 · Ratio of incomes and expenditures with equal savings · Mediumमध्यम

    The monthly incomes of Lakshmi and Aditya are in the ratio 7 : 6, and their expenses are in the ratio 4 : 1. If each saves ₹8,500 a month, what is Lakshmi’s monthly income?

    1. ₹2,000
    2. ₹9,000
    3. ₹10,500
    4. ₹59,500
    Answer:उत्तर: ₹10,500
    1. 7x − 4y = 6x − 1y ⇒ 1x = 3y ⇒ y = 1x/3.
    2. Substitute in 7x − 4y = 8,500 to get x = 1,500.
    3. Lakshmi’s income = 7 × 1,500 = ₹10,500.

  5. Example 5उदाहरण 5 · Ratio of incomes and expenditures with equal savings · Mediumमध्यम

    The monthly incomes of Arjun and Kabir are in the ratio 9 : 7, and their expenses are in the ratio 9 : 5. If each saves ₹3,600 a month, what is Arjun’s monthly income?

    1. ₹3,600
    2. ₹5,600
    3. ₹7,200
    4. ₹32,400
    Answer:उत्तर: ₹7,200
    1. 9x − 9y = 7x − 5y ⇒ 2x = 4y ⇒ y = 2x/4.
    2. Substitute in 9x − 9y = 3,600 to get x = 800.
    3. Arjun’s income = 9 × 800 = ₹7,200.

  6. Example 6उदाहरण 6 · Ratio of incomes and expenditures with equal savings · Mediumमध्यम

    The monthly incomes of Lakshmi and Diya are in the ratio 7 : 6, and their expenses are in the ratio 8 : 5. If each saves ₹3,250 a month, what is Lakshmi’s monthly income?

    1. ₹2,000
    2. ₹4,500
    3. ₹5,250
    4. ₹22,750
    Answer:उत्तर: ₹5,250
    1. 7x − 8y = 6x − 5y ⇒ 1x = 3y ⇒ y = 1x/3.
    2. Substitute in 7x − 8y = 3,250 to get x = 750.
    3. Lakshmi’s income = 7 × 750 = ₹5,250.

Common mistakesआम गलतियाँ

  • Using the same unknown for incomes and expenses.
  • Giving the expense or the other person’s income instead of the one asked for.
  • Treating savings as a share of income in the income ratio.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न

How do I solve income and expenditure ratio questions?

Write incomes as ax and bx and expenses as cy and dy. Equal savings gives ax − cy = bx − dy; solve for x and y, then compute what is asked.

How do I combine A : B and B : C?

Make the B terms equal by multiplying each ratio, then read off A : B : C.

Is ratio important for SSC?

Yes. Ratio and proportion appears directly and inside partnership, ages, mixtures and DI questions.

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