Profit, loss, discount

1. Ye topic hai kya?

CP = jo tumne diya (cost). SP = jo mila (selling). SP > CP → profit; SP < CP → loss. MP (marked / list) tag pe likha; discount MP se kat-ta, CP se nahi. Average ne CP 200, SP 250 bheja tha — % yahan CP ke 100 pe.

Paper yahan kya maangta

P% L% SP CP reverse, “12 ka SP = 10 ka CP”, MP se discount, successive 10% phir 20%, tagged +40% phir 10% off, do articles same SP +r/−r, 900 g ko 1 kg, buy-n-get-1.

Yahan kya nahi

25% of 80, population, pass marks — Percentage. PRT/100, years — Simple interest. Cricket 80 — Average. 8:12:15 — Ratio. Milk alligation — Mixture. Capital×time — Partnership.

Profit% / loss% ka base hamesha CP. Discount% ka base hamesha MP. SP = CP × (100±r)/100. CP = SP × 100/(100±r).

2. CP, SP, % — kyun CP neeche

Profit paisa = SP − CP. Percent = (profit / CP) × 100. 50/250 = 20% galat — 250 SP hai. Sahi 50/200 = 25%. Percentage chapter: “reference neeche”; yahan shop ka reference cost hai, selling nahi (unless paper “on SP” likhe — rare).

Average / Percentage P10 yahi pair. 25% of 80 alag sawal (sirf of). Yahan 50 cost ke 200 ka chhota hissa.

Maang	Formula
SP, profit r%	CP × (100+r)/100
SP, loss r%	CP × (100−r)/100
CP from SP, profit r%	SP × 100/(100+r)
CP from SP, loss r%	SP × 100/(100−r)

“12 oranges ka SP = 10 ka CP” → 12 SP = 10 CP → SP/CP = 10/12. Loss = 2/12 = 16⅔%. Ulta: 10 ka SP = 12 ka CP → profit 20%.

Example

CP 200, SP 250. Profit %?

Solution

50/200
25%. 50/250=20 trap. 25% of 80 Percentage.

Answer25%

Example

CP 200, 20% loss. SP?

Solution

×0.80
160. 200−20=180 mat (20% ≠ ₹20).

Answer160

Example

SP 240, 20% profit. CP?

Solution

×100/120
200. 240−20% of 240 = 192 — galat base SP.

Answer200

Example

12 ka SP = 10 ka CP. Loss %?

Solution

10/12
Loss 1/6 = 16⅔%. Cricket 80 nahi.

Answer16⅔%

3. Marked price, discount, successive off

Tag MP. Customer SP = MP − discount. Discount% = (disc / MP)×100. Profit ab bhi CP se. Shop 40% upar mark kare, 10% off de — pehle MP, phir cut, phir CP se P%.

Successive discounts a% phir b%: net = a + b − ab/100. 10% phir 20% → 28%, 30% nahi. Percentage ke +20/−20 (salary) alag pair; yahan dono cuts same direction. SI ke years nahi.

MP 100 → 90 → 72. Net 28% off. Percentage 100→120→96 (+20 then −20) yahan mat ghusao.

CP = 100, mark 40%, then 10% off: MP=140, SP=126, profit=26%. (40−10=30 mat.)

Buy 4 get 1 free = 5 cheezein, pay 4. Discount 1/5 = 20% (MP same maano).

Example

MP 800, 15% discount. SP?

Solution

×0.85
680. 15% of 800=120, 800−120. Base MP.

Answer680

Example

10% phir 20% discount. Net?

Solution

10+20−2
28%. 30 trap. +20/−20 wala −4% Percentage.

Answer28%

Example

CP 100, MP +40%, 10% off. Profit %?

Solution

SP 126
26%. 30 mix mark−off.

Answer26%

4. Do articles, false weight, chain sale

Do cheezein same SP, ek r% profit, ek r% loss → net loss r²/100 %. SP 100-100, r=10: loss 1%. Same CP pe +10 aur −10 to net 0 — yahan CP alag-alag (loss wale ka CP bada). Percentage +10/−10 ek salary pe −1% alag kahani.

False weight: 900 g ko 1 kg becha, rate “no profit”. Usne 900 ka maal 1000 ke paise mein diya. Profit 100/900 = 11⅑%. Agar 10% profit bhi claim kare: SP = 110 per 1000-label, CP of 900 = 90 (agar 1 kg CP=100) → profit 20/90 ≈ 22.2% — pehle actual CP of goods sold.

Farq 100 g. Profit on CP of 900, tag 1000 pe nahi. Mixture milk-water nahi.

A ne B ko 10% profit, B ne C ko 10%. C ne 121 diya. A ka CP = 121 / (1.1×1.1) = 100. Net 21% A se C, 20% nahi. Compound interest ke saal yahan nahi — do sales.

Discount CP pe mat. Profit SP pe mat (jab tak “on SP” na ho). Successive off jod ke 30 mat. False weight ko HCF 900,1000 mat. 8:12:15 ratio chain nahi.

Example

Same SP, +10% aur −10%. Net?

Solution

r²/100
1% loss. Same-CP +10/−10 = 0 — alag.

Answer1% loss

Example

900 g as 1 kg, no claimed profit. Actual profit %?

Solution

100/900
11⅑%.

Answer11⅑%

Example

A→B 10%, B→C 10%. C pays 121. A ka CP?

Solution

/1.21
100. SI 2 saal nahi.

Answer100

5. Sawal — basic se pro

Q1 · Basic

CP 200, SP 250. Profit %?

25%
20%
50%
250%

Solution

50/200
25%. B SP-base.

Answer25%

Q2 · Basic

CP 200, 20% loss. SP?

Solution

×0.8
160. B ₹20 cut.

Answer160

Q3 · Basic

SP 240, 20% profit. CP?

Solution

240×5/6
200. B 20% of SP.

Answer200

Q4 · Medium

12 ka SP = 10 ka CP. Loss %?

16⅔%
20%
12%
10%

Solution

2/12
16⅔%. B 10 ka SP = 12 ka CP mix.

Answer16⅔%

Q5 · Medium

MP 800, 15% off. SP?

Solution

800−120
680.

Answer680

Q6 · Medium

10% phir 20% off. Net?

Solution

a+b−ab/100
28%. D +20/−20 mix.

Answer28%

Q7 · Medium

Mark +40%, 10% off. Profit % (CP=100)?

Solution

126−100
26%.

Answer26%

Q8 · Pro

Same SP, +10% aur −10%. Net?

1% loss
0
1% profit
10% loss

Solution

r²/100
1% loss. B same-CP trap.

Answer1% loss

Q9 · Pro

900 g as 1 kg. Profit %?

11⅑%
10%
11%
9%

Solution

100/900
11⅑%.

Answer11⅑%

Q10 · Pro

5 innings 32, 6th se avg 40. Is chapter?

Nahi — Average
Haan, profit 80
Discount 40
SI 32

Solution

Cricket
A. 80 wahan.

AnswerA

Practice

Pehle khud, phir neeche kholo.

1 2 3 4 5 6 7 8 9 10

Buy 4 get 1 free. Discount %?

Solution

1/5
20%. B 1/4 (pay 4, free 1 ko 4 pe).

Answer20%

A→B 10%, B→C 10%. C=121. A CP?

Solution

/1.21
100.

Answer100

10 ka SP = 12 ka CP. Profit %?

20%
16⅔%
12%
10%

Solution

12/10
20%. B Q4 ulta.

Answer20%

CP 480, SP 408. Loss %?

Solution

72/480
15%.

Answer15%

800 g as 1 kg, claims 10% profit. Actual %? (1 kg CP=100)

37.5%
10%
25%
12.5%

Solution

CP 80, SP 110
30/80=37.5%.

Answer37.5%

10% off ke baad 25% profit. MP, CP se kitna % upar?

38⁸⁄₉%
35%
15%
25%

Solution

1.25 CP = 0.9 MP
MP/CP=125/90 → 38⁸⁄₉% upar.

Answer38⁸⁄₉%

MP 400, 25% off. SP?

Solution

×0.75
300. 25% of 80 Percentage nahi.

Answer300

Profit 25%. SP=250. CP?

200
187.5
225
312.5

Solution

×4/5
200. Q1 ulta.

Answer200

25% of 80. Is chapter?

Nahi — Percentage
Haan, CP 80
Discount 20
HCF 20

Solution

of
A. 20 wahan. Yahan CP-base.

AnswerA

P10

P=1000, r=10%, t=2, SI. Is chapter?

Nahi — Simple interest
Haan, profit 200
Discount 2 yr
False weight

Solution

PRT/100
A. Agle topic.

AnswerA