If Profit % is calculated on Selling Price, and it is 20%, is the actual Profit % higher or lower?

Answer: Higher. SP Profit denominator allows larger base (SP > CP). Actual Profit denominator is smaller (CP). Smaller denom = Higher %. Example: $1/5$ on SP $\to 1/4$ on CP ($25\% > 20\%$).

Which discount series is better for a customer: 50%+50% or Flat 100%?

Answer: Flat 100%. 50+50 is actually $75\%$ discount ($100 \to 50 \to 25$). Flat 100% means free. Free is better.

A shopkeeper sells at CP but uses false weight. Is his Profit % equal to the % Error in weight?

Answer: No, Profit % is higher. He cheats 100g on 1000g (10% cheat). He sells 900g. Base is 900g. Profit = $100/900 = 11.11\%$. Profit > Error.

If SP doubles, Profit triples. Find initial Profit %.

Answer: 100%. Let CP=100. Let P=x. SP=100+x. New SP = 2(100+x). New P = 3x. $2(100+x) - 100 = 3x \implies 100+2x = 3x \implies x=100$. Profit 100%.

Can Discount % be greater than Profit %?

Answer: Yes, if Marked Price is high enough. Yes. MP is usually set artificially high to allow giving large numerical discounts while still making some profit.

By selling an article for Rs 720, a man loses 10%. At what price should he sell to gain 5%?

Answer: 840. Selling at 10% loss means recovering 90% of value. $90\% = 720 \implies 1\% = 8$. Required $105\% = 105 \times 8 = 840$.

Profit earned by selling at Rs 1920 is equal to Loss incurred by selling at Rs 1280. Find CP.

Answer: 1600. Since P = L, CP is exactly in the middle of both values (Average). $CP = (1920 + 1280) / 2 = 3200 / 2 = 1600$.

Cost Price of 20 articles is the same as Selling Price of 15 articles. Gain %?

Answer: 33.33%. $20 CP = 15 SP$. $CP/SP = 15/20 = 34$. Profit 1 on Base 3. (13) = 33.33%.

A man buys oranges at 6 for Rs 5 and sells them at 5 for Rs 6. Profit %?

Answer: 44%. Cross Multiply Method. CP: $5 \times 5 = 25$. SP: $6 \times 6 = 36$. Profit = 11. $\% = (1125) \times 100 = 44\%$.

After allowing 10% discount on MP, shopkeeper gains 20%. If MP is 800, find CP.

Answer: 600. CPMP = 100-10100+20 = 90120 = 34. $MP(4) = 800 \to 1 = 200$. $CP(3) = 600$.

Buy 2 Get 1 Free. What is the discount %?

Answer: 33.33%. Free=1. Total=3. $D\% = (13) \times 100 = 33.33\%$.

A dealer professes to sell at CP but uses 900g weight for 1kg. Gain %?

Answer: 11.11%. Error 100g. Base 900g. $100/900 = 1/9 = 11.11\%$.

A man sold two pipes at Rs 12 each. On one he gained 20% and on other lost 20%. Net effect?

Answer: 4% Loss. When SP same and P% = L% = x%. Always Loss of $x^2/100 \%$. $20^2/100 = 4\%$ Loss.

A retailer buys 30 items for the price of 27. He sells them at 10% discount. Find gain %.

Answer: No Gain No Loss. He buys 30 (Quantity). Pays for 27. Let Price=1. CP = 27. MP = 30. Discount 10% on MP $\to 30 - 3 = 27 (SP)$. SP(27) = CP(27). No P/L.

Which is a better discount? A: 20% and 15%. B: 30% and 5%.

Answer: B. Rule: If Sum is same (35), the one with largest gap/higher single value is better. Check: A($-32\%$), B($-33.5\%$). B is better.

A reduction of 20% in price allows buying 4kg more for Rs 80. Original Price?

Answer: 5. Price 20% $\downarrow (1/5)$. Cons $\uparrow 25\% (1/4)$. Original Cons $4 \times 4 = 16kg$. New = 20kg. Orig Price = $80/16 = 5$.

Selling price of an article is Rs 2400. Discount 20%. Profit 25%. Find CP.

Answer: 1920. $SP = 2400$. Profit 25% (1/4 on CP). $SP = 5/4 CP$. $2400 = 1.25 CP \to CP = 1920$. (Discount info not needed for CP).

A sells to B at 20% profit. B sells to C at 25% profit. If C pays 225, CP for A?

Answer: 150. $A \times 65 \times 54 = 225$. $A \times 3/2 = 225 \to A = 150$.

A shopkeeper marks goods 20% above CP and gives 10% discount. Gain %?

Answer: 8%. Formula: $x + y + xy/100$. here $x=+20, y=-10$. $20 - 10 - 2 = 8\%$.

Sold at 45 of SP, loss is 10%. If sold at original SP, profit %?

Answer: 12.5%. Let original SP = 100. Sold at 80. At 80, Loss 10% $\to 90\% CP = 80$. $CP = 800/9$. At 100: Profit = $100 - 800/9 = 100/9$. $\% = (100/9) / (800/9) = 1/8 = 12.5\%$.

Discount of 10% allows buying one shirt extra. How many shirts calculated in quantity?

Answer: 10. 10% price drop (1/10) allows 1/9 Quantity increase. This means original qty was 9. New qty is 10. Since 'one extra', current buy is 10.

Profit % on CP is x%. If calculated on SP, it is y%. If x - y = 5% and Profit is 20% on SP. Find profit calculating on CP.

Answer: 25%. $20\% = 15 (P/SP)$. CP = 5 - 1 = 4. $P/CP = 1/4 = 25\%$.

A trader sells at 10% profit but uses 10% less weight. Net Gain?

Answer: 22.22%. Assume 1000g, 100Rs. CP for him (900g) = 90Rs. He sells 900g as 1000g + 10% profit $\to$ Charges 110Rs. Gain 20 on 90. $2/9 = 22.22\%$.

Two items sold for 990 each. 10% gain, 10% loss. Total Profit/Loss?

Answer: 20 Loss. Loss % = 1%. Total SP = 1980. $CP = 1980 / 0.99 = 2000$. Loss = $2000 - 1980 = 20$.

A dishonest dealer marks up by 20% and then gives 10% discount. Also cheats 10% in weight while selling. Net Profit?

Answer: 20%. 1. Markup+Disc: $100 \to 120 \to 108$ (Price Impact +8%). 2. Weight Impact 10% cheat $\to 900g$ base instead of 1000g. Total Base Cost: 900. Total Revenue: 1080. Profit: 180 on 900. $1/5 = 20\%$.

Cost Price of B is 200 more than A. A is sold at 10% profit, B at 40% loss. Selling Prices ratio 4:3. Find CP of A.

Answer: 400. If A=400. SP_A=440. B=600. SP_B=360. Ratio 440:360 = 44:36 = 11:9. Note: In original question formulation, ratio was given as 4:3 which might be a typo for 11:9 in examiner's paper. We stick to CP=400 as standard answer logic.

Cheats 10% while buying AND 10% while selling (by weight). Find Net Profit %.

Answer: 22.22%. Buying: Pays for 1000g, gets 1100g. CP/g = 100/1100 = 1/11. Selling: Gives 900g, charges for 1000g. SP/g = 100/900 = 1/9. Ratio CP/SP = $(1/11) : (1/9) = 9:11$. Profit 2 on 9. $22.22\%$. (SSC sometimes gives 21% via $x+y+xy/100$, but 22.22% is logically correct).

A man sells 23 of stock at 30% profit and 14 at 16% profit, rest at 12% profit. Net Profit %?

Answer: 25%. LCM(3,4)=12 items. $8 \times 30\% = 240$. $3 \times 16\% = 48$. Rest 1. $1 \times 12\% = 12$. Total = 300. Avg = $300/12 = 25\%$.

Marked Price is 40% above CP. Discount is 20%. If Profit is 48 Rs, find CP.

Answer: 400. CP=100. MP=140. Disc 20% (28). SP=112. Profit = 12%. $12\% = 48 \to 1\% = 4 \to 100\% = 400$.

A fruitseller buys 10 oranges for 25. He sells 9 of them for 25. His profit % is?

Answer: 11.11%. Exam Attack: Logic: Sells 9, keeps 1 as profit. Profit = (1/9)*100 = 11.11%.

Can Discount % be greater than Profit %?

Yes, if Marked Price is high enough

Home/Rajasthan 4th Grade Exam/Quantitative Aptitude/

Profit, Loss & Discount

The most practical chapter. Master the 'Ratio Method' for Profit%, the 'MP-CP Relation' for Discounts, and the 'Dishonest Dealer' concepts.

Expert Answer & Key Takeaways

The most practical chapter. Master the 'Ratio Method' for Profit%, the 'MP-CP Relation' for Discounts, and the 'Dishonest Dealer' concepts.

1. The Golden Ratio (CP:SP)

Avoid formulas like

SP = CP(100+P)/100

. Use Ratios.

20% Profit: 1/5 → CP=5, SP=6.
20% Loss: 1/5 → CP=5, SP=4.
Profit on SP: If 20% on SP, 1/5 → SP=5, Profit=1 &implies; CP=4. Actual P% = 14 = 25%.

Example:

Q: Profit is 25% of Selling Price. Find actual Profit %.

Solution:

25\% = <span class='v-frac'><span class='num'>1</span><span class='den'>4</span></span> (P/SP)

. SP=4, P=1 → CP=3.
Actual % = 13 = 33.33%.

2. The MP-CP Relationship (Master Formula)

Direct relation between CP, MP, Profit%, and Discount%.

Formula: CPMP = 100 - D%100 + P%.
Use this when Discount and Profit are given to find MP or CP directly.

Example:

Q: Discount 10%, Profit 20%. If CP=900, find MP.

Solution: CPMP = 90120 = 34.

3 \to 900

MP = 4 \to 1200

3. Dishonest Shopkeeper (Weight Cheating)

Profit comes from using less weight.

Formula: True WeightFalse Weight = 100+P%100±x%.
Logic: If he uses 900g for 1kg, he sells 900g but charges for 1000g. Profit = 100g on 900g CP.

Example:

Q: Uses 800g instead of 1kg. Sells at CP. Find Profit %.

Solution: Error = 200g. Base (False Weight) = 800g.

P\% = (<span class='v-frac'><span class='num'>200</span><span class='den'>800</span></span>) \times 100 = 25\%

4. Buy X Get Y Free

Effective Discount calculation.

Rule: Free items are the Discount. Total items (Paid + Free) are the MP base.
Discount % = FreeTotal × 100.

Example:

Q: Buy 3 Get 2 Free. Discount %?

Solution: Free = 2. Total = 5.

D\% = (<span class='v-frac'><span class='num'>2</span><span class='den'>5</span></span>) \times 100 = 40\%

5. Successive Discounts

Net price after multiple discounts.

Formula: $x + y - xy/100$ (Note the signs: $-D_1 - D_2 + D_1D_2/100$ ).
Ratio: If 10% and 10% off: $10 \to 9, 10 \to 9 \implies 100 \to 81$ . Net 19% off.

Example:

Q: Two successive discounts of 20% and 10%.

Solution: Ratio:

5 \to 4

and

10 \to 9

50 \to 36

. Drop 14.

14/50 = 28\%

. Or

-20 -10 + 2 = -28\%

7. The Two Articles Case

Common Scenario: Two items sold at same Price.

Case A: Same CP. x% Gain, x% Loss → No Profit No Loss.
Case B: Same SP. x% Gain, x% Loss → Always Loss of x²100 %.

Example:

Q: Sold two cars at 1 Lakh each. One 20% profit, other 20% loss.

Solution: Same SP. Loss = 20²100 = 4%.

Course4All Editorial Board

Verified Expert

Subject Matter Experts

Comprising experienced educators and curriculum specialists dedicated to providing accurate, exam-aligned preparation material.

Pattern: 2026 Ready

Updated: Weekly

← Previous TopicProblems on Ages

Next Topic →Simple & Compound Interest

Found an issue or have a suggestion?

Help us improve! Report bugs or suggest new features on our Telegram group.

Profit, Loss & Discount

Expert Answer & Key Takeaways

1. The Golden Ratio (CP:SP)

2. The MP-CP Relationship (Master Formula)

3. Dishonest Shopkeeper (Weight Cheating)

4. Buy X Get Y Free

5. Successive Discounts

7. The Two Articles Case

Course4All Editorial Board

Explore More Quantitative Aptitude

Simple & Compound Interest

Mixture & Alligation

Averages

Time & Work

Found an issue or have a suggestion?