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Profit–Loss–Discount Based Data Sufficiency

Introduction

Profit-Loss-Discount Data Sufficiency प्रश्न यह पूछते हैं कि क्या दिए गए statements से ऐसे मान निकाले जा सकते हैं कि cost price (CP), selling price (SP), marked price (MP), profit%, या discount% निर्धारित किए जा सकते हैं।

ये प्रश्न जानकारी की पर्याप्तता (sufficiency) पर केंद्रित होते हैं, न कि लंबी गणना पर - आपको यह तय करना होता है कि कोई unique numerical answer किसी statement से अकेले मिल सकता है या दोनों को जोड़ना पड़ेगा।

Pattern: Profit–Loss–Discount Based Data Sufficiency

Pattern

मुख्य विचार यह है कि statements को निम्न मूल संबंधों में map करें:
SP = CP × (1 + profit%),
SP = MP × (1 - discount%),
Profit% = (SP - CP) ÷ CP × 100.

परखें कि क्या कोई statement target निकालने के लिए सभी आवश्यक variables देता है (उदाहरण के लिए, CP निकालने के लिए SP और profit% चाहिए या MP और discount% जिससे SP मिल सके)।

Step-by-Step Example

Question

किसी article का cost price (CP) क्या है?
(I) Selling price (SP) = ₹1,200 और profit = 20%।
(II) Marked price (MP) = ₹1,500 और discount = 20%।

सही विकल्प चुनें:
A. केवल (I) पर्याप्त है
B. केवल (II) पर्याप्त है
C. प्रत्येक statement अकेला पर्याप्त है
D. दोनों statements साथ में आवश्यक हैं

Solution

  1. Step 1: Statement (I) analyze करें

    SP = ₹1,200 और profit = 20% ⇒ SP = CP × 1.20।
    इसलिए CP = SP ÷ 1.20 = ₹1,200 ÷ 1.20 = ₹1,000 → (I) अकेला sufficient है।

  2. Step 2: Statement (II) analyze करें

    MP = ₹1,500 और discount = 20% ⇒ SP = MP × 0.80 = 1,500 × 0.80 = ₹1,200।
    अब SP ज्ञात है, और CP (जैसा ऊपर) निकाला जा सकता है: CP = ₹1,200 ÷ 1.20 = ₹1,000 → (II) अकेला भी sufficient है।

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    दोनों (I) और (II) स्वतन्त्र रूप से SP = ₹1,200 और CP = ₹1,000 देते हैं ✅

Quick Variations

1. यदि SP और discount% दिया हो - CP निकालने के लिए कभी-कभी profit% कहीं और से चाहिए होती है।

2. MP और profit% दिए हों - आपको MP → SP में discount या अन्य सूचना से convert करना पड़ सकता है।

3. दो statements अलग-अलग profit% और discount% के रूप में दिए हों - इन्हें combine कर के CP या SP isolate करना पड़ सकता है।

4. Worded financial contexts: successive discounts, VAT/सैल्स टैक्स जो discount के बाद add हो (इन्हें additional multiplicative factor की तरह treat करें)।

Trick to Always Use

  • Step 1: Percentages को जल्दी से multipliers में बदलें (उदाहरण: +20% → ×1.20; -20% → ×0.80)।
  • Step 2: सीधे उस सूत्र को लिखें जिसकी आपको ज़रूरत है (उदाहरण: CP = SP ÷ multiplier या SP = MP × multiplier)।
  • Step 3: देखें क्या कोई single statement उस सूत्र के लिए सभी inputs देता है - अगर हाँ तो वह sufficient है।
  • Step 4: शक होने पर symbolic या numeric रूप में मान निकाल कर देखें कि क्या unique answer मिलता है।

Summary

Summary

  • Profit/discount प्रतिशतों को तुरंत multiplicative factors (जैसे ×1.20, ×0.80) में बदलें।
  • कोई statement तभी पर्याप्त है जब वह target सूत्र के सभी inputs दे।
  • जब एक statement relation दे और दूसरा missing numeric value दे, तब दोनों को combine करें।
  • Uniqueness की पुष्टि के लिए symbolic या numeric जाँच जल्दी करें।

याद रखने वाला उदाहरण:
(I) SP = ₹1,200 & profit 20% ⇒ CP = ₹1,000; (II) MP = ₹1,500 & discount 20% ⇒ SP = ₹1,200 ⇒ CP = ₹1,000.

Practice

(1/5)
1. What is the cost price (CP) of an article?<br>(I) Selling price (SP) = ₹1,125 and profit = 12.5%.<br>(II) Marked price (MP) = ₹1,250 and discount = 10%.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    SP = ₹1,125 and profit = 12.5% ⇒ SP = CP × 1.125 ⇒ CP = 1,125 ÷ 1.125 = ₹1,000 → (I) alone is sufficient.

  2. Step 2: Analyze (II)

    MP = ₹1,250 and discount = 10% ⇒ SP = 1,250 × 0.90 = ₹1,125. (II) gives SP but without profit% it cannot directly give CP unless profit% known → (II) alone is insufficient.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    From (I): CP = 1,125 ÷ 1.125 = 1,000 ✅
Hint: Convert profit% to multiplier (12.5% → 1.125) then divide SP by multiplier to get CP.
Common Mistakes: Assuming MP→SP info automatically gives CP without profit% data.
2. What is the discount percentage offered on an article?<br>(I) Cost price (CP) = ₹600 and profit = 20%.<br>(II) Marked price (MP) = ₹1,000 and selling price (SP) = ₹850.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    CP = ₹600 and profit = 20% ⇒ SP = 600 × 1.20 = ₹720. (I) gives SP but MP is unknown → cannot compute discount% → (I) insufficient.

  2. Step 2: Analyze (II)

    MP = ₹1,000 and SP = ₹850 ⇒ discount% = ((1,000 - 850) ÷ 1,000) × 100 = (150 ÷ 1,000) × 100 = 15% → (II) alone is sufficient.

  3. Final Answer:

    Only (II) is sufficient → Option B

  4. Quick Check:

    Discount% = 150/1,000 = 0.15 = 15% ✅
Hint: When MP and SP are given, discount% = (MP - SP) ÷ MP × 100 directly.
Common Mistakes: Using CP and profit% to infer discount% without MP.
3. What is the selling price (SP) of an article?<br>(I) Cost price (CP) = ₹400 and profit = 25%.<br>(II) Marked price (MP) = ₹625 and discount = 20%.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    SP = CP × (1 + profit%) = 400 × 1.25 = ₹500 → (I) alone is sufficient.

  2. Step 2: Analyze (II)

    SP = MP × (1 - discount%) = 625 × 0.80 = ₹500 → (II) alone is also sufficient.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    Both (I) and (II) give SP = ₹500 independently ✅
Hint: Use SP = CP × (1 + profit%) or SP = MP × (1 - discount%) whichever is available.
Common Mistakes: Failing to convert percent to multiplier before computing.
4. What is the cost price (CP) of an article?<br>(I) Marked price (MP) = ₹2,500 and discount = 20%.<br>(II) Profit = 25% on the cost price.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    MP = ₹2,500 and discount = 20% ⇒ SP = 2,500 × 0.80 = ₹2,000. (I) gives SP but CP unknown → insufficient.

  2. Step 2: Analyze (II)

    Profit = 25% ⇒ SP = CP × 1.25 → without SP numeric, CP cannot be found → (II) insufficient.

  3. Step 3: Combine

    From (I): SP = ₹2,000. From (II): CP = SP ÷ 1.25 = 2,000 ÷ 1.25 = ₹1,600 → both together are necessary.

  4. Final Answer:

    Both statements together are necessary → Option D

  5. Quick Check:

    SP 2,000 and profit 25% ⇒ CP = 2,000 ÷ 1.25 = 1,600 ✅
Hint: Use MP→SP via discount, then SP→CP via profit% when needed.
Common Mistakes: Trying to compute CP from profit% without a numeric SP or vice versa.
5. What is the marked price (MP) of an article?<br>(I) Selling price (SP) = ₹720 after a discount of 10%.<br>(II) Cost price (CP) = ₹576 and profit = 25%.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    SP = ₹720 after discount 10% ⇒ MP = SP ÷ 0.90 = 720 ÷ 0.90 = ₹800 → (I) alone is sufficient to find MP.

  2. Step 2: Analyze (II)

    CP = 576 and profit = 25% ⇒ SP = 576 × 1.25 = ₹720 → (II) gives SP but discount not given, though (II) independently yields SP = 720; however MP requires discount data → (II) alone is insufficient for MP.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    MP = 720 ÷ 0.9 = 800 ✅
Hint: MP = SP ÷ (1 - discount%). If SP and discount% are given, MP follows directly.
Common Mistakes: Using CP & profit% alone to infer MP without discount info.

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