Q1. Define Marked Price (MP).

Ans: MP is the price printed on the item's price-tag.

Q2. Define Discount.

Ans: Discount is the amount subtracted from MP while selling.

Q3. Formula for Discount amount when discount is \(x\%\).

Ans: \(\text{Discount} = \text{MP}\times\dfrac{x}{100}.\)

Q4. Formula for Selling Price (SP).

Ans: \(\text{SP} = \text{MP}\left(1-\dfrac{x}{100}\right).\)

Q5. If MP = ₹100 and discount = \(15\%\), SP = ?

Ans: \(100\times(1-0.15)=₹85.\)

Q6. If MP = ₹360 and SP = ₹306, discount = ?

Ans: Discount = \(360-306=₹54.\)

Q7. If discount = ₹54 on MP ₹360, discount \% = ?

Ans: \(\dfrac{54}{360}\times100=15\%\) (written inside MathJax as 15\%).

Q8. MP = ₹1200, discount \(=10\%\). Discount = ?

Ans: \(1200\times0.10=₹120.\)

Q9. MP = ₹1200, discount \(=10\%\). SP = ?

Ans: \(1200-120=₹1080.\)

Q10. SP = ₹1120 after \(20\%\) discount. MP = ?

Ans: MP \(=1120/(1-0.20)=1120/0.8=₹1400.\)

Q11. If decided price = ₹100, marked 30\% higher (₹130) then 20\% discount, final SP = ?

Ans: \(130\times0.8=₹104\) (which is \(+4\%\) over ₹100).

Q12. MP = ₹1750, discount \(=8\%\). SP = ?

Ans: Discount = \(1750\times0.08=₹140\). SP = \(1750-140=₹1610.\)

Q13. SP = ₹1610 and seller made \(15\%\) profit. Cost price (CP) = ?

Ans: CP = \(1610/1.15=₹1400.\)

Q14. Define Commission.

Ans: Commission is the percent-based fee paid to an agent for selling goods.

Q15. Commission formula for rate \(r\%\) on amount \(A\).

Ans: \(\text{Commission}=A\times\dfrac{r}{100}.\)

Q16. Broker gets \(2\%\) on ₹2,50,000 from buyer and again from seller. Total brokerage = ?

Ans: \(250000\times0.02=5000\) each ⇒ total \(=₹10000.\)

Q17. Agent commission \(=1\%\) on ₹40,500. Commission = ?

Ans: \(40500\times0.01=₹405.\)

Q18. What is a rebate?

Ans: Rebate is a special discount (sometimes government-compensated); treated same as discount in calculations.

Q19. Rebate \(=15\%\) on ₹1800 → rebate amount = ?

Ans: \(1800\times0.15=₹270.\)

Q20. After ₹270 rebate on ₹1800, amount payable = ?

Ans: \(1800-270=₹1530.\)

Q1. Book: MP = ₹360, SP = ₹306. Find discount\% (show steps).

Ans: Discount = \(360-306=54.\) Discount\% \(=\dfrac{54}{360}\times100=15\%.\)

Q2. Chair: MP = ₹1200, discount \(=10\%\). Find discount & SP (two methods).

Ans: Discount = \(1200\times0.10=₹120\). SP = \(1200-120=₹1080\). (Alt: SP = \(1200\times0.9=1080\)).

Q3. Saree: SP = ₹1120 after \(20\%\) discount. Find MP.

Ans: MP = \(1120/0.8=₹1400.\)

Q4. Price ↑30\% then discount 20\% on tagged price. If decided price = ₹100, find final percent change.

Ans: MP = 130 ⇒ SP = \(130\times0.8=104\) ⇒ \(+4\%\) over decided price.

Q5. MP = ₹1750, discount \(8\%\), profit \(15\%\) on CP. Find CP.

Ans: SP = \(1750\times0.92=₹1610.\) CP = \(1610/1.15=₹1400.\)

Q6. Decided price 100, MP = +25\%, discount 20\%, final price = ? Gain/ loss?

Ans: MP=125 ⇒ SP=125×0.8=100 ⇒ no gain/no loss ⇒ 0\%.

Q7. MP = ₹1700, SP = ₹1540. Find discount and discount\%.

Ans: Discount = \(1700-1540=₹160\). Discount\% = \(160/1700\times100\approx9.4118\%\).

Q8. MP = ₹990, discount 10\% → SP = ?

Ans: SP = \(990\times0.9=₹891.\)

Q9. SP = ₹900 after 20\% discount. MP = ?

Ans: MP = \(900/0.8=₹1125.\)

Q10. Fan MP = ₹3000, discount 12\%: discount & SP?

Ans: Discount = \(3000\times0.12=₹360.\) SP = \(3000-360=₹2640.\)

Q11. Mixer: MP ₹2300 bought at ₹1955. Discount\% = ?

Ans: Discount=345 ⇒ \(\dfrac{345}{2300}\times100=15\%.\)

Q12. If SP = CP = ₹22,250 after giving 11\% discount, find MP.

Ans: SP = MP×0.89 ⇒ MP = \(22250/0.89=₹25000.\)

Q13. If 10\% of MP = ₹17, find MP & SP.

Ans: MP = \(17/0.10=₹170.\) SP = \(170-17=₹153.\)

Q14. Rebate 15\% on ₹1800 → rebate & payable?

Ans: Rebate = \(1800\times0.15=₹270.\) Payable = \(1800-270=₹1530.\)

Q15. Broker 2\% on ₹2,50,000 from both sides — total broker gets?

Ans: Each side \(=250000\times0.02=₹5000\). Total \(=₹10000.\)

Q16. Agent sold 10 qtls at ₹4050/qtl, commission 1\% — amount received?

Ans: Sale = \(40500\). Commission \(=40500\times0.01=₹405.\) Seller gets \(40500-405=₹40095.\)

Q17. John sells books worth ₹4500, commission 15\% — commission = ?

Ans: \(4500\times0.15=₹675.\)

Q18. Rafique sold ₹15000 of flowers, agent gets 4\%. Commission and received?

Ans: Commission = \(15000\times0.04=₹600.\) Rafique receives \(15000-600=₹14400.\)

Q19. Farmer sold for ₹9200, agent 2\% — agent gets ?

Ans: \(9200\times0.02=₹184.\)

Q20. Umatai: 3 sarees ₹560 each, 6 honey ₹90 each, rebate 12\% — payable?

Ans: Total = \(3\times560 + 6\times90 =1680+540=₹2220.\) Rebate = \(2220\times0.12=₹266.4.\) Payable = \(2220-266.4=₹1953.6.\)

Q1. Marked 25\% above CP, then 12\% discount. If CP = ₹100, final profit\%?

Ans: MP = 125. SP = \(125\times(1-0.12)=125\times0.88=110.\) Profit = \(110-100=10\) ⇒ \(10\%\) profit.

Q2. MP = ₹1500, discount 15\%. If CP = ₹1200, find discount amount, SP and profit\%.

Ans: Discount = \(1500\times0.15=₹225.\) SP = \(1275.\) Profit = \(1275-1200=₹75.\) Profit\% = \(75/1200\times100=6.25\%.\)

Q3. SP = ₹900 after 10\% discount. Seller claims 20\% profit. Find CP and MP.

Ans: CP = \(900/1.2=₹750.\) MP = \(900/0.9=₹1000.\)

Q4. Successive discounts 10\% and 5\% on MP ₹2000. Net discount\% and SP?

Ans: After first: 1800. After second: \(1800\times0.95=₹1710.\) Net discount = \(2000-1710=₹290\) ⇒ net \% = \(290/2000\times100=14.5\%.\)

Q5. CP = ₹22500, MP = CP +25\%, discount 10\% — final SP and profit\%?

Ans: MP = \(22500\times1.25=28125.\) SP = \(28125\times0.9=25312.5.\) Profit = \(25312.5-22500=2812.5.\) Profit\% = \(2812.5/22500\times100=12.5\%.\)

Q6. Trader wants 20\% profit and gives 10\% discount. MP as \% of CP?

Ans: Need SP = \(1.20\)CP, SP = MP×0.90 ⇒ MP = \(1.20/0.90\cdot CP = \tfrac{4}{3}CP = 133.\overline{3}\%\) of CP.

Q7. Rebate 12\% on ₹2220. Payable?

Ans: \(2220\times0.12=₹266.4.\) Payable \(=2220-266.4=₹1953.6.\)

Q8. Commission 2.5\% on ₹48,000. Commission and amount to owner?

Ans: Commission \(=48000\times0.025=₹1200.\) Amount remitted \(=48000-1200=₹46800.\)

Q9. MP ₹1800, 20\% off then extra 5\% off. Final price and net discount\%?

Ans: After 20\% ⇒ \(1440.\) After 5\% ⇒ \(1440\times0.95=1368.\) Net discount \(=1800-1368=432\) ⇒ net \% = \(432/1800\times100=24\%.\)

Q10. Seller received ₹735000 after paying 2\% brokerage. Find sale price S.

Ans: Seller got \(0.98S=735000\Rightarrow S=735000/0.98=₹750000.\)

Q11. Mark up 40\% then give 30\% discount. CP=100 → gain/loss?\

Ans: MP=140 ⇒ SP=98 ⇒ loss \(=2\%\).

Q12. Agent 3\% on ₹1,20,000. Commission and remitted?

Ans: Commission \(=120000\times0.03=₹3600.\) Remitted \(=120000-3600=₹116400.\)

Q13. Dress MP ₹2400, 50\% off then 10\% extra off — final price?

Ans: After 50\% ⇒ 1200. After 10\% ⇒ \(1200\times0.9=₹1080.\)

Q14. Shopkeeper wants 12\% profit after giving 15\% discount. MP as \% of CP?

Ans: Need SP = \(1.12\)CP and SP = MP×0.85 ⇒ MP = \(1.12/0.85\cdot CP \approx131.7647\%\) of CP.

Q15. Cloth CP ₹280, MP +20\%, discount 10\% — SP & profit\%?

Ans: MP = 336, SP = 336×0.9 = 302.4, Profit = 22.4 ⇒ Profit\% = \(22.4/280\times100=8\%.\)

Q16. Want 25\% gain and give 10\% discount — MP as \% of CP?

Ans: MP = \(1.25/0.90\cdot CP \approx138.888\%\) of CP.

Q17. Seller sold for ₹40500 via agent 1\% — seller gets ?

Ans: Commission = \(40500\times0.01=₹405.\) Seller gets \(40500-405=₹40095.\)

Q18. Discount 15\% makes SP = ₹3400. MP = ?

Ans: MP = \(3400/0.85=₹4000.\)

Q19. Trade discount 20\% then cash discount 5\% on net from MP ₹1200 — final price?

Ans: After 20\% ⇒ 960; then 5\% ⇒ 960×0.95=912.

Q20. Car sold ₹750000; 2\% brokerage from both buyer and seller. Broker gets ? Buyer pays ?

Ans: Brokerage each = \(750000\times0.02=₹15000.\) Broker total = ₹30000. Buyer pays \(750000+15000=₹765000\) if buyer pays brokerage.

Example: MP = ₹360, SP = ₹306. Discount\%?

Ans: Discount = \(54\). Discount\% = \(54/360\times100=15\%\).

Example: MP = ₹1200, discount \(10\%\). SP?

Ans: SP \(=1200(1-0.10)=₹1080.\)

Practice: MP ₹1700, SP ₹1540. Discount?

Ans: ₹160.

Practice: John sold books ₹4500 at 15\% commission. Commission?

Ans: ₹675.

Practice: Broker 2\% on ₹750000 from both sides. Total brokerage and buyer's payment?

Ans: Brokerage each = ₹15000, total = ₹30000. Buyer pays ₹765000 (if buyer pays brokerage).