Ch 7: Profit, Loss & Discount | Maths

Dosto, ye chapter roz ki zindagi ka Maths hai — kitne mein khareeda (CP), kitne mein becha (SP), kitna fayda ya nuksaan hua, aur "50% OFF" wali sale mein asli chhoot kitni hai.

CET Group D mein isse 1–2 questions pakke aate hain. Aur khushi ki baat — ye pura chapter Chapter 4 (Percentage) par hi khada hai. Successive discount ka formula toh wahi hai jo waha padha tha!

Sirf ek baat gaanth baandh lo: Profit/Loss ka % hamesha CP par, aur Discount ka % hamesha MP par. Ye ek line 80% galtiyan bacha degi. Chalo shuru! 💪

1. Teen Zaroori Shabd

Short	Naam	Matlab
CP	Cost Price (Kray Mulya)	Jitne mein khareeda
SP	Selling Price (Vikray Mulya)	Jitne mein becha
MP	Marked Price (Ankit Mulya)	Tag/list par likha daam (discount isi par milta hai)

Profit (Laabh) = SP − CP (jab SP bada ho)
Loss (Haani) = CP − SP (jab CP bada ho)
Discount = MP − SP

2. Formulas — ⭐ Dil se yaad karo

⭐ Profit/Loss ka % hamesha CP par Profit% = (Profit ÷ CP) × 100 · Loss% = (Loss ÷ CP) × 100
SP = CP × (100 + P%)/100 · SP = CP × (100 − L%)/100
CP = SP × 100/(100 + P%) · CP = SP × 100/(100 − L%)

✏️ Solved Example 1 — CP ₹500, SP ₹600 Step 1: Profit = 600 − 500 = ₹100
Step 2: Profit% = (100 ÷ 500) × 100 = 20% ✓ (neeche CP, SP nahi!)

✏️ Solved Example 2 — SP ₹720, profit 20%. CP? Step 1: CP = SP × 100/(100 + 20) = 720 × 100/120
Step 2: = ₹600 ✓ (check: 600 + 20% = 720 ✓)

✏️ Solved Example 3 — SP ₹480, loss 20%. CP? Step 1: CP = 480 × 100/(100 − 20) = 480 × 100/80
Step 2: = ₹600 ✓ (loss mein neeche 80 aata hai, 120 nahi!)

3. Discount (Chhoot)

⭐ Discount ka % hamesha MP par Discount% = (Discount ÷ MP) × 100 · SP = MP × (100 − d%)/100

✏️ Solved Example — MP ₹800, discount 25% Step 1: SP = 800 × 75/100 = ₹600 ✓
Ulta sawal: MP 1200 aur SP 960 → discount% = (240 ÷ 1200) × 100 = 20%

4. Successive Discount (do baar chhoot)

⭐ Single equivalent discount = a + b − (a × b)/100 Solved Example: 20% aur 10% ke do discount = kitna ek discount?
Step 1: 20 + 10 − (20×10)/100 = 30 − 2 = 28% ✓
Check: MP 1000 → 800 → 720, yani 280 ki chhoot = 28% ✓
⚠️ 30% NAHI hota — ye Chapter 4 wala hi successive-change formula hai.

5. Marked Price + Discount + Profit (mila-jula sawal)

✏️ Solved Example — CP se 25% upar mark, phir 10% discount Step 1: CP = 100 maan lo (hamesha 100 maano!) → MP = 125
Step 2: SP = 125 × 90/100 = 112.5
Step 3: Profit = 112.5 − 100 = 12.5 → Profit% = 12.5% ✓

6. Dishonest Shopkeeper (kam taul)

⭐ Gain% = [Error ÷ (Sahi weight − Error)] × 100 Solved Example: Dukaandar 1 kg ki jagah 900 g deta hai (par daam 1 kg ka leta hai). Uska fayda?
Step 1: Error = 1000 − 900 = 100 g
Step 2: Gain% = (100 ÷ 900) × 100 = 11.11% (yaani 11⅑%) ✓
Soch: neeche wo aata hai jo usne asal mein diya (900), na ki 1000.

7. Ek Aur Kaam ka Rule

📌 Do cheezein same daam par, ek +x% aur ek −x% Hamesha NUKSAAN hota hai, aur loss% = x²/100. Jaise 20% par 4% ka nuksaan — bilkul Chapter 4 wale successive rule jaisa.

✏️ Type 1 — "20 cheezon ka CP = 16 cheezon ka SP" Step 1: Formula: Profit% = [(CP wali ginti − SP wali ginti) ÷ SP wali ginti] × 100
Step 2: = (20 − 16)/16 × 100 = 25% profit ✓
Soch: 16 bech ke 20 ka paisa mil gaya — 4 ka extra, jo 16 par 25% hai. (Ginti ulti ho to loss hota hai.)

✏️ Type 2 — Do cheezein same SP, ek fayda ek nuksaan Do article ₹1200-1200 mein beche; ek par 20% fayda, dusre par 20% nuksaan. Net?
Step 1: Pehle ka CP = 1200 × 100/120 = 1000 · Dusre ka = 1200 × 100/80 = 1500
Step 2: Total CP = 2500, total SP = 2400 → nuksaan ₹100
Step 3: Loss% = 100/2500 × 100 = 4% ✓ (= x²/100 = 400/100, shortcut!)

✏️ Type 3 — "₹100 zyada milte to fayda hota" Ek cheez 10% nuksaan mein bechi. Agar ₹100 zyada milte to 15% fayda hota. CP?
Step 1: CP = C maano → 0.90C + 100 = 1.15C
Step 2: 100 = 0.25C → C = ₹400 ✓
Check: SP1 = 360, SP2 = 460, antar 100 ✓
Shortcut: ₹100 = (10 + 15)% = 25% of CP → CP = 400.

✏️ Type 4 — Discount ke baad bhi profit Dukaandar CP se 40% upar mark karta hai aur 25% discount deta hai. Profit%?
Step 1: CP = 100 → MP = 140 → SP = 140 × 75/100 = 105
Step 2: Profit = 5% ✓ (yaad rakho: CP hamesha 100 maano — sabse fast tarika)

✏️ Type 5 — Kam taul (false weight) "1 kg ki jagah 800 g deta hai" → Gain% = 200/800 × 100 = 25%
"1 kg ki jagah 950 g" → 50/950 × 100 = 5.26%
Formula ek hi: Error ÷ (jitna asal mein diya) × 100.

Trick 1: CP ko 100 maan lo
CP = 100 → sab % seedha rupaya
"25% upar mark, 10% discount" → 100 → 125 → 112.5 → profit 12.5%. Variables ka jhanjhat khatam — ye is chapter ka sabse bada hathiyar hai!

Trick 2: Fraction se profit% (Ch 3-4 ka jod)
25% = 1/4 · 20% = 1/5 · 12.5% = 1/8
"CP 800 par 25% profit" → 800 ka 1/4 = 200 → SP = 1000. Division se tez, dimaag mein hi ho jata hai.

Trick 3: Successive discount = Ch 4 wala formula
a + b − ab/100
20% + 10% = 28% · 10% + 10% = 19% · 20% + 20% = 36%. Ye teen combos exam mein baar-baar aate hain — ratt lo!

Trick 4: Same SP, +x% aur −x% → hamesha loss
Loss% = x²/100
10% → 1%, 20% → 4%, 25% → 6.25%. Answer mein "no profit no loss" wala option hamesha galat hota hai!

Trick 5: CP nikalne mein neeche kya aata hai
Profit → 100+P · Loss → 100−L
SP 720 @20% profit → 720 × 100/120 = 600. SP 480 @20% loss → 480 × 100/80 = 600. Ulta lagaya to answer galat!

❌ Galti 1: Profit% SP par nikal dena CP 500, SP 600 → profit% = 100/500 = 20%, na ki 100/600 = 16.67%. Profit/Loss ka base hamesha CP hai. (Discount ka base MP hai — dono alag!)

❌ Galti 2: Do discounts jod dena 20% + 10% = 30% NAHI, 28% hai. Aur 50% + 50% = 100% (muft!) bilkul nahi — wo 75% hota hai.

❌ Galti 3: Loss mein (100 + L) laga dena SP 480 par 20% loss → CP = 480 × 100/80 = 600. Agar 120 laga diya to answer 400 aa jayega — pura galat.

❌ Galti 4: Same-SP wale sawal mein "barabar" sochna Ek par 20% fayda, dusre par 20% nuksaan (same SP) → net 4% ka NUKSAAN, barabar nahi. Ye CET ka favourite trap hai.

❌ Galti 5: Kam taul mein 1000 ko neeche lagana 900 g dene par gain = 100/900 = 11.11%, na ki 100/1000 = 10%. Neeche jitna maal asal mein diya wo aata hai.

Profit% ka formula?tap 👆

(Profit ÷ CP) × 100

Discount% kis par nikalta hai?tap 👆

MP par — (Discount ÷ MP) × 100

SP nikalo (CP aur P% se)tap 👆

CP × (100+P)/100

CP nikalo (SP aur P% se)tap 👆

SP × 100/(100+P)

CP nikalo (SP aur L% se)tap 👆

SP × 100/(100−L)

SP nikalo (MP aur discount se)tap 👆

MP × (100−d)/100

Successive discount a%, b% = ?tap 👆

a + b − ab/100

20% + 10% discount = ?tap 👆

28% (30% nahi)

Same SP, +x% & −x% → net?tap 👆

x²/100 % ka LOSS

Kam taul (false weight) gain%?tap 👆

Error / (sahi − error) × 100

900 g dene par gain%?tap 👆

100/900 × 100 = 11⅑%

CP of 20 = SP of 16 → profit%?tap 👆

(20−16)/16 × 100 = 25%

MP kya hota hai?tap 👆

Tag par likha daam — discount isi par

25% upar mark, 10% discount → profit?tap 👆

100 → 125 → 112.5 = 12.5%

50% + 50% successive discount = ?tap 👆

75% (100% nahi!)

Profit ho to SP aur CP mein bada kaun?tap 👆

SP > CP (loss mein CP > SP)

10% + 10% discount = ?tap 👆

19%

Sawal solve karne ka sabse fast tarika?tap 👆

CP = 100 maan lo

Cheez	Formula
Profit / Loss	SP − CP / CP − SP
Profit% · Loss%	(Profit ÷ CP) × 100
Discount%	(Discount ÷ MP) × 100
SP (profit se)	CP(100+P)/100
CP (profit se)	SP × 100/(100+P)
CP (loss se)	SP × 100/(100−L)
SP (discount se)	MP(100−d)/100
Successive discount	a + b − ab/100
20%+10% · 10%+10% · 50%+50%	28% · 19% · 75%
Same SP, +x% & −x%	x²/100 % loss
False weight gain%	Error/(sahi − error) × 100
CP of m = SP of n	(m−n)/n × 100 % profit

🎯 Score: 0 / 0 Total questions: 14

Practice (exam-style)

Q1. An article bought for ₹500 is sold for ₹600. The profit percent is:

💡 Profit 100 ÷ CP 500 × 100 = 20% (SP par nahi!).

Practice (exam-style)

Q2. An article costing ₹400 is sold at a profit of 15%. Its selling price is:

💡 400 × 115/100 = 460.

Practice (exam-style)

Q3. An article is sold for ₹720 at a profit of 20%. Its cost price is:

💡 720 × 100/120 = 600.

Practice (exam-style)

Q4. An article is sold for ₹480 at a loss of 20%. Its cost price is:

💡 480 × 100/80 = 600 (loss mein neeche 80).

Practice (exam-style)

Q5. The marked price of an article is ₹800 and a discount of 25% is given. The selling price is:

💡 800 × 75/100 = 600.

Practice (exam-style)

Q6. Two successive discounts of 20% and 10% are equivalent to a single discount of:

💡 20+10−(200/100) = 28% (1000 → 800 → 720).

Practice (exam-style)

Q7. The marked price of an article is ₹1200 and it is sold for ₹960. The rate of discount is:

💡 Discount 240 ÷ MP 1200 × 100 = 20%.

Practice (exam-style)

Q8. Two articles are sold at ₹1200 each; one at a gain of 20% and the other at a loss of 20%. The net result is:

💡 CPs 1000 + 1500 = 2500, SP 2400 → 4% loss (x²/100).

Practice (exam-style)

Q9. If the cost price of 20 articles is equal to the selling price of 16 articles, the profit percent is:

💡 (20−16)/16 × 100 = 25% profit.

Practice (exam-style)

Q10. A shopkeeper marks his goods 25% above the cost price and allows a discount of 10%. His profit percent is:

💡 CP 100 → MP 125 → SP 112.5 → profit 12.5%.

Practice (exam-style)

Q11. A dishonest shopkeeper uses a weight of 900 g for 1 kg. His gain percent is:

💡 100/900 × 100 = 11.11% (neeche 900, 1000 nahi).

Practice (exam-style)

Q12. An article is sold at a loss of 10%. Had it been sold for ₹100 more, there would have been a gain of 15%. The cost price is:

💡 ₹100 = (10+15)% = 25% of CP → CP = 400 (SP 360 aur 460).

Practice (exam-style)

Q13. An article is sold for ₹450 at a profit of 25%. The cost price is:

💡 450 × 100/125 = 360.

Practice (exam-style)

Q14. A cycle bought for ₹1500 is sold for ₹1200. The loss percent is:

💡 Loss 300 ÷ CP 1500 × 100 = 20%.

Do line jo pura chapter hain: Profit/Loss ka % CP par aur Discount ka % MP par. CP nikalte waqt neeche (100+P) ya (100−L) — ye ulta hua to answer galat. Har mila-jula sawal mein CP = 100 maan lo, sab kuch rupaye mein dikhne lagega (25% mark + 10% discount → 12.5% profit). Do discounts kabhi jodo mat: a + b − ab/100 (20%+10% = 28%). Same daam par ek +x% aur ek −x% bechne par hamesha x²/100 % ka nuksaan hota hai. Aur kam-taul wale sawal mein neeche wahi aata hai jitna maal asal mein diya (900 g → 11⅑%). 🚀