Practice Mode•Instant Explanations & 50:50 Enabled
Percentage Profit Loss MCQs
High-yield multiple choice questions asked in previous years (UPSC, SSC CGL, JKSSB, RRB & State PSCs).
High-Yield Concept Capsule & Key Facts
📌 Foundational commercial arithmetic pillar in SSC CGL/CHSL, IBPS PO/Clerk, RRB NTPC, and State PSC exams.
Percentage Foundations & Fraction-to-Percentage Equivalents
- • Fraction Equivalents: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 1/11 = 9.09%, 1/12 = 8.33%.
- • Percentage Change: ((Final - Initial) / Initial) × 100.
- • Successive Percentage Changes: Effective Rate = a + b + (ab / 100)%. (Treat discounts as negative values: -d1 - d2 + (d1×d2/100)).
- • Expenditure Constant Rule: If price of an item increases by r%, consumption must be reduced by [r / (100 + r)] × 100% to keep expenditure constant.
Profit, Loss & Discount Arithmetic
- • Profit = Selling Price (SP) - Cost Price (CP). Profit % = (Profit / CP) × 100.
- • Loss = CP - SP. Loss % = (Loss / CP) × 100. (Always calculated on CP unless stated otherwise).
- • Marked Price (MP) & Discount: Discount = MP - SP. Discount % = (Discount / MP) × 100.
- • Direct Formula linking MP and CP: (MP / CP) = (100 + Profit %) / (100 - Discount %).
- • Dishonest Dealer Concept: When a merchant uses a false weight of 'W' grams instead of standard 'S' grams: Gain % = [(Error) / (True Value - Error)] × 100 = [(S - W) / W] × 100.
| Concept | Standard Formula | Exam Shortcut |
|---|---|---|
| Profit Percentage | (SP - CP) / CP × 100 | If SP is 6/5 of CP, profit is 1/5 = 20% |
| Loss Percentage | (CP - SP) / CP × 100 | If SP is 4/5 of CP, loss is 1/5 = 20% |
| Successive Discounts | d1 + d2 - (d1 × d2 / 100) | Two 20% discounts = 20 + 20 - 4 = 36% |
| Marked vs Cost Price | MP / CP = (100 + P%) / (100 - D%) | Direct single-step ratio calculation |
| Dishonest Merchant | Gain % = (Error / False Weight) × 100 | Gives 900g for 1kg => (100/900) × 100 = 11.11% |
| Price-Consumption | Reduction % = [r / (100 + r)] × 100 | Price +25% => Consumption -[25/125]= -20% |
Showing 15 Practice Questions
Q1High-Yield Practice SetMedium
A shopkeeper sells an article for Rs. 540 and incurs a loss of 10%. At what price should he sell it to gain 20%?
Q2High-Yield Practice SetMedium
If the price of sugar increases by 25%, by what percentage must a household reduce its consumption so that total expenditure remains unchanged?
Q3High-Yield Practice SetMedium
A merchant marks his goods 30% above the cost price and allows a discount of 15% on the marked price. Find his overall profit percentage.
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Q4High-Yield Practice SetMedium
Two items are sold for Rs. 990 each. On one, the seller gains 10% and on the other, he loses 10%. In the whole transaction, the seller:
Q5High-Yield Practice SetMedium
A dishonest grocer claims to sell his pulses at cost price, but uses a false weight of 950 grams for a 1 kilogram measure. His profit percentage is:
Q6High-Yield Practice SetMedium
Successive discounts of 20%, 10%, and 5% are equivalent to a single discount of:
Q7High-Yield Practice SetMedium
If the cost price of 12 pens is equal to the selling price of 8 pens, find the profit percentage.
Q8High-Yield Practice SetMedium
A trader buys two articles for Rs. 2,000 each. He sells one at a profit of 20% and the other at a loss of 20%. What is his overall gain or loss percentage?
Q9High-Yield Practice SetMedium
A bicycle marked at Rs. 4,500 is sold for Rs. 3,825. What is the discount percentage offered on the bicycle?
Q10High-Yield Practice SetMedium
By selling 33 metres of cloth, a shopkeeper gains the selling price of 11 metres. What is his profit percentage?
Q11High-Yield Practice SetMedium
A man spends 35% of his income on food, 25% on children's education, and 80% of the remainder on house rent. What percentage of his income is left with him?
Q12High-Yield Practice SetMedium
If the length of a rectangle is increased by 20% and its breadth is decreased by 10%, the percentage change in area is:
Q13High-Yield Practice SetMedium
A manufacturer sells an article to a wholesale dealer at a profit of 10%. The wholesale dealer sells it to a shopkeeper at 20% profit. The shopkeeper sells it to a customer for Rs. 56,100 at 15% loss. Find the cost of manufacture for the manufacturer.
Q14High-Yield Practice SetMedium
In an examination, 35% of candidates failed in English and 40% failed in Mathematics. If 20% failed in both subjects, what percentage of candidates passed in both subjects?
Q15High-Yield Practice SetMedium
A pressure cooker is sold at a profit of 16%. If it had been sold for Rs. 20 more, the profit would have been 20%. The cost price of the cooker is:
Frequently Asked Questions (Percentage Profit Loss)
Q: Why is profit or loss percentage always calculated on the Cost Price (CP)?
Cost Price represents the actual capital investment made by the merchant. The return on investment (profit or loss) must be evaluated against the initial base outlay, which is the Cost Price. Only when a question specifically stipulates 'profit on selling price' do you use SP as the denominator.
Q: What is the single equivalent discount for successive discounts of 20% and 10%?
Using the successive change formula: Effective Discount = d1 + d2 - (d1 × d2 / 100). For 20% and 10%: Effective = 20 + 10 - (20 × 10 / 100) = 30 - 2 = 28%.
Q: If two articles are sold at the same price, one at x% profit and the other at x% loss, what is the net result?
When two articles have the same Selling Price (SP) and one is sold at x% profit while the other at x% loss, there is ALWAYS an overall net loss given by Loss % = (x / 10)^2 %.
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