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Quantitative Aptitudeमात्रात्मक योग्यता · लाभ और हानि

Profit and Lossलाभ और हानि questions and answersप्रश्न और उत्तर

Profit and loss questions mix three prices (cost, marked and selling) and two bases. Once you know which base each percentage uses, they become one-line calculations.

  • Unlimitedअसीमित fresh questionsनए प्रश्न
  • Answersउत्तर always one tap awayहमेशा एक टैप दूर
  • 4 subtopicsउप-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 profit and loss worksलाभ और हानि को समझिए

Profit and loss percentages are calculated on the cost price. Discount is calculated on the marked (list) price. Most wrong answers come from mixing these two bases.

Think in multipliers: a 20% profit means SP = 1.2 × CP; a 10% discount means SP = 0.9 × MP. Chain the multipliers instead of computing each price.

When two articles are sold at the same price, one at x% profit and one at x% loss, there is always an overall loss of x²/100 %.

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।

Mental mathsमानसिक गणितRarely taughtकम सिखाई जाने वाली✓ Checked on 40 cases✓ 40 मामलों पर जाँची गई

Rise by 1/n, fall by 1/(n + 1)

Use it when:कब इस्तेमाल करें: “Price rises by x%. By how much must consumption fall to keep spending the same?” or “by what % must it fall to get back?”

  1. Write the rise as a unit fraction 1/n (25% = 1/4, 20% = 1/5, 12.5% = 1/8).
  2. The fall that cancels it is 1/(n + 1) (1/5 = 20%, 1/6 = 16.67%, 1/9 = 11.11%).
Exampleउदाहरण

Sugar costs 25% more. By what % must a family cut consumption to spend the same?

→ 25% = 1/4 → cut 1/5 = 20%.

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

Why:क्यों: (1 + 1/n) × (1 − 1/(n + 1)) = ((n + 1)/n) × (n/(n + 1)) = 1, so the two changes cancel exactly.

Limits:सीमाएँ: Works directly for unit fractions. For other rises use r/(100 + r) × 100 (a 30% rise needs a 300/13 ≈ 23.08% cut).

Mental mathsमानसिक गणितRarely taughtकम सिखाई जाने वाली✓ Checked on 5 cases✓ 5 मामलों पर जाँची गई

Turn every % into a fraction multiplier, then cancel

Use it when:कब इस्तेमाल करें: Any chain of increases, decreases, discounts or taxes.

  1. Rewrite each change as a fraction: +20% → 6/5, −25% → 3/4, +12.5% → 9/8, −10% → 9/10.
  2. Multiply the fractions and cancel before computing anything.
Exampleउदाहरण

Marked 20% above cost, sold at 25% discount. Profit or loss?

→ 6/5 × 3/4 = 18/20 = 9/10 → 10% loss.

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

Why:क्यों: Each percentage change multiplies the value by (1 ± r/100); a fraction is just that multiplier written exactly, and products of fractions cancel.

Limits:सीमाएँ: Best when the percentages are “fraction friendly” (multiples of 5, 12.5, 16.67, 33.33). For 17% or 23% use the decimal 1.17 / 0.77.

Formulaसूत्रRarely taughtकम सिखाई जाने वाली✓ Checked on 1,200 cases✓ 1,200 मामलों पर जाँची गई

Same selling price, a% gain on one and b% loss on the other

Use it when:कब इस्तेमाल करें: Two articles sold at the same price, one at a gain and one at a loss, and the gain and loss are not equal.

  1. Overall % = (100(a − b) − 2ab) / (200 + a − b).
  2. A negative answer is a loss. When a = b this becomes −a²/100, the well-known special case.
Exampleउदाहरण

Two phones sold for ₹9,900 each, one at 10% gain and one at 10% loss.

→ (0 − 200)/200 = −1% → 1% loss.

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

Why:क्यों: If each sells at S, the costs are S/(1 + a) and S/(1 − b). Overall profit = 2S / (S/(1 + a) + S/(1 − b)) − 1, which simplifies to (a − b − 2ab)/(2 + a − b) with a, b as fractions.

Limits:सीमाएँ: Only when both selling prices are equal. If the cost prices are equal instead, the overall % is simply (a − b)/2.

Formulaसूत्रRarely taughtकम सिखाई जाने वाली✓ Checked on 432 cases✓ 432 मामलों पर जाँची गई

How far above cost to mark, for profit p after discount d

Use it when:कब इस्तेमाल करें: “A shopkeeper wants p% profit after giving d% discount. How much above cost should he mark?”

  1. Markup % = 100(p + d) / (100 − d).
Exampleउदाहरण

Profit 20% after a 20% discount: mark up by?

→ 100 × 40 / 80 = 50% above cost.

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

Why:क्यों: MP × (1 − d) = CP × (1 + p) ⇒ MP/CP = (1 + p)/(1 − d); subtracting 1 gives (p + d)/(1 − d).

Limits:सीमाएँ: d must be below 100%. Works with a loss too: use a negative p.

Formulaसूत्र✓ Checked on 841 cases✓ 841 मामलों पर जाँची गई

Bought x for ₹1, sold y for ₹1

Use it when:कब इस्तेमाल करें: “Bought oranges at 10 for ₹1 and sold them at 8 for ₹1. Profit %?”

  1. Profit % = (x − y) / y × 100. A negative answer is a loss.
Exampleउदाहरण

Bought 10 for ₹1, sold 8 for ₹1

→ (10 − 8)/8 × 100 = 25% profit

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

Why:क्यों: Cost per item is 1/x and selling price per item is 1/y; (1/y − 1/x)/(1/x) = (x − y)/y.

Limits:सीमाएँ: Assumes the same money unit on both sides; for “x for ₹p, y for ₹q” compare p/x with q/y.

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 · Marked price, discount and profit · Easyआसान

    A dealer in Lucknow marks goods 50% above the cost price and gives a discount of 10%. What is the profit or loss percentage?

    1. 40% profit
    2. 35% profit
    3. 35% loss
    4. 37.5% profit
    Answer:उत्तर: 35% profit
    1. Let CP = ₹100. MP = ₹150.
    2. SP = 150 × 90/100 = ₹135.
    3. Result: 35% profit.

  2. Example 2उदाहरण 2 · Same selling price, x% gain and x% loss · Easyआसान

    Joseph sold two sewing machines for the same price. On one there was a gain of 10% and on the other a loss of 10%. What is the overall result?

    1. No profit, no loss
    2. 1% loss
    3. 1% gain
    4. 2% loss
    Answer:उत्तर: 1% loss
    1. Loss % = x²/100 = 100/100 = 1%.
    2. This is always a loss, whatever the selling price.

  3. Example 3उदाहरण 3 · Successive discounts: one equivalent discount · Easyआसान

    A shop gives successive discounts of 10%, then 10% on the marked price. What single discount is equivalent?

    1. 10%
    2. 19%
    3. 20%
    4. 21%
    Answer:उत्तर: 19%
    1. Fractions left: 0.9 × 0.9 = 0.81.
    2. So 81% of the marked price is paid.
    3. Equivalent single discount = 100% − 81% = 19%.

  4. Example 4उदाहरण 4 · Dishonest dealer: false weights, mark-ups and discounts · Easyआसान

    Saanvi, who runs a dry-fruit seller, sells rice at cost price but uses a weight of 900 g instead of 1 kg. What is the actual profit percentage?

    1. 10%
    2. 11.11%
    3. 12.61%
    4. 14.11%
    Answer:उत्तर: 11.11%
    1. Money received for “1 kg”: 1 × cost price of 1 kg.
    2. Cost of what he actually gives: 0.9 × cost price of 1 kg.
    3. Profit factor = 1000/900 = 1.1111, so the profit is 11.11%.

  5. Example 5उदाहरण 5 · Marked price, discount and profit · Mediumमध्यम

    An electronics store in Kochi offers successive discounts of 30% and 20% on a festive sale. What single discount is equivalent to these?

    1. 25%
    2. 44%
    3. 50%
    4. 47%
    Answer:उत्तर: 44%
    1. 30 + 20 − 600/100
    2. = 50 − 6 = 44%.

  6. Example 6उदाहरण 6 · Same selling price, x% gain and x% loss · Mediumमध्यम

    Diya sold two bicycles for the same price. On one there was a gain of 25% and on the other a loss of 25%. What is the overall result?

    1. 6.25% gain
    2. 6.25% loss
    3. 2.5% loss
    4. No profit, no loss
    Answer:उत्तर: 6.25% loss
    1. Loss % = x²/100 = 625/100 = 6.25%.
    2. This is always a loss, whatever the selling price.

  7. Example 7उदाहरण 7 · Successive discounts: one equivalent discount · Mediumमध्यम

    A shop gives successive discounts of 15%, then 10% on the marked price. What single discount is equivalent?

    1. 15%
    2. 23.5%
    3. 25%
    4. 26.5%
    Answer:उत्तर: 23.5%
    1. Fractions left: 0.85 × 0.9 = 0.765.
    2. So 76.5% of the marked price is paid.
    3. Equivalent single discount = 100% − 76.5% = 23.5%.

  8. Example 8उदाहरण 8 · Dishonest dealer: false weights, mark-ups and discounts · Mediumमध्यम

    Tenzin, who runs a dry-fruit seller, marks his goods 25% above cost price, sells at the marked price and uses a 750 g weight for every kilogram. What is the actual profit percentage?

    1. 25%
    2. 33.33%
    3. 58.33%
    4. 66.67%
    Answer:उत्तर: 66.67%
    1. Money received for “1 kg”: 1.25 × cost price of 1 kg.
    2. Cost of what he actually gives: 0.75 × cost price of 1 kg.
    3. Profit factor = 1.25 × 1000/750 = 1.6667, so the profit is 66.67%.

Common mistakesआम गलतियाँ

  • Calculating profit % on the selling price.
  • Applying a discount on the cost price.
  • Assuming equal profit and loss cancel out.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न

Is profit percentage calculated on cost price or selling price?

On cost price, unless the question clearly says otherwise.

What is the marked price formula?

MP = CP × (100 + profit %) / (100 − discount %).

What is a dishonest dealer question?

A seller uses a false weight, so the cost of what is actually given is less than what is charged. Profit % = (true weight − false weight) / false weight × 100.

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