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Simple interest

Lesson 92 of 113

1. Ye topic hai kya?

Simple interest = sirf asal (principal) pe, har saal wahi extra. Interest ke upar interest nahi — woh Compound interest, agle pe. Paper: SI = PRT/100, amount A = P + SI, P/R/T dhoondho, 18 mahine, double kab, do alag rates. Profit-loss P10 yahi bheja: P=1000, r=10%, t=2.

Paper yahan kya maangta

SI aur A, missing P/R/T, t months/days, paisa double/triple/4-guna, SI ∝ t, do time pe amount se P nikaalo, pehle 5% phir 8% (abhi bhi simple — joddo).

Yahan kya nahi

CP 200 SP 250, 10%+20% off — Profit/loss. Year-2 pe interest of 1100 — Compound. 25% of 80 — Percentage. Cricket 80 — Average. Capital×time share — Partnership.

SI = (P × R × T) / 100 · A = P + SI
T saal mein. 18 months = 3/2. 73 din (365-day year) = 1/5. R percent per annum.

2. PRT — kyun seedha line

Har saal extra = PR/100. Do saal = 2× wahi. Graph seedha. 1000 pe 10%: pehla saal +100, doosra +100, SI=200, A=1200. CI mein doosra saal 110 hota — yahan nahi.

1000 1100 1200 0 1 yr 2 yr

P=1000, 10% SI. Har saal +100. Seedha. CI agle chapter — wahan year-2 1210.

MaangUlta
PSI × 100 / (R×T)
RSI × 100 / (P×T)
TSI × 100 / (P×R)
Example

P=1000, R=10%, T=2. SI aur A? (Profit-loss P10 yahi.)

Solution

  1. PRT/100

    1000×10×2 / 100 = 200. A=1200. CP–SP 250 nahi. CI 210 nahi.

AnswerSI 200, A 1200
Example

SI=240, R=8%, T=3. P?

Solution

  1. ×100/(RT)

    240×100 / 24 = 1000.

Answer1000
Example

P=800, R=5%, T=4. SI?

Solution

  1. 800×5×4/100

    160.

Answer160

3. Months, days, double / triple

T hamesha year. 18 months = 18/12 = 3/2. 8 months = 2/3. 73 days / 365 = 1/5 (paper 365 le, leap mat ghusao jab tak na likhe).

Amount = n × P ⇒ SI = (n−1)P ⇒ R T = 100(n−1).
Double (n=2): RT=100, T=100/R. R=5% → 20 saal.
Triple (n=3): RT=200. 8 saal mein 3-guna → R=25%.
4-guna: RT=300.

SI time ke proportional: 3 saal 450 ⇒ 1 saal 150 ⇒ 5 saal 750. (CI mein aisa seedha scale nahi.)

Example

P=1000, R=8%, T=18 months. SI?

Solution

  1. T=3/2

    1000×8×1.5 / 100 = 120. 18×8 mat (T saal).

Answer120
Example

5% SI pe double kab?

Solution

  1. T=100/R

    20 saal. CI Rule-72 agle pe.

Answer20 years
Example

8 saal mein 3-guna. R?

Solution

  1. SI=2P

    2P = P×R×8/100 → R=25%.

Answer25%

4. Do rates, do amounts

Pehle 2 saal 5%, phir 3 saal 8%, P=1000 — abhi bhi simple: SI = 1000×5×2/100 + 1000×8×3/100 = 100+240 = 340. Compound nahi (koi 5% ke baad nayi principal nahi).

Amount 4 saal baad 1200, 6 saal baad 1400. Farq 200 = 2 saal ka SI ⇒ 100/saal. 4 saal SI=400 ⇒ P = 1200−400 = 800. R = 100×100/(800×1) = 12.5%.

T ko months rehne mat do. A ko SI mat samjho. Double pe R=50% mat (wo 2 saal ka galat shortcut). 10% phir 20% discount Profit/loss. Year-2 pe 10% of 1100 Compound.
Example

1000: 5% × 2 yr + 8% × 3 yr. SI?

Solution

  1. Add

    100+240=340. 13%×5=650 trap (rates mix).

Answer340
Example

A after 4 yr = 1200, after 6 yr = 1400. P?

Solution

  1. 200 / 2 yr

    100/yr. 4 yr SI=400. P=800.

Answer800

5. Sawal — basic se pro

Q1 · Basic

P=1000, R=10%, T=2. SI?

  1. 200
  2. 210
  3. 20
  4. 1200

Solution

  1. 200

    B CI year-2. D amount.

Answer200
Q2 · Basic

Uska amount?

  1. 1200
  2. 200
  3. 1000
  4. 1100

Solution

  1. P+SI

    1200. D 1 year.

Answer1200
Q3 · Basic

SI=240, R=8%, T=3. P?

  1. 1000
  2. 576
  3. 2400
  4. 80

Solution

  1. 24000/24

    1000.

Answer1000
Q4 · Medium

P=800, R=5%, T=4. SI?

  1. 160
  2. 200
  3. 32
  4. 960

Solution

  1. 160

    .

Answer160
Q5 · Medium

5% pe double. Kitne saal?

  1. 20
  2. 5
  3. 10
  4. 2

Solution

  1. 100/5

    20. C 50% mix.

Answer20
Q6 · Medium

1000, 8%, 18 months. SI?

  1. 120
  2. 1440
  3. 80
  4. 240

Solution

  1. T=1.5

    120. B T=18.

Answer120
Q7 · Medium

A(4 yr)=1200, A(6 yr)=1400. P?

  1. 800
  2. 1200
  3. 1000
  4. 200

Solution

  1. 100/yr

    P=800. D farq.

Answer800
Q8 · Pro

8 saal, 3-guna. R?

  1. 25%
  2. 12.5%
  3. 37.5%
  4. 8%

Solution

  1. 200/8

    25%. B double mix (100/8).

Answer25%
Q9 · Pro

1000: 5%×2 + 8%×3. SI?

  1. 340
  2. 650
  3. 400
  4. 240

Solution

  1. 100+240

    340. B 13×5.

Answer340
Q10 · Pro

CP 200, SP 250. Is chapter?

  1. Nahi — Profit / loss
  2. Haan, SI 50
  3. R=25% t=1
  4. Amount 250

Solution

  1. Shop

    A. 25% wahan CP-base.

AnswerA

Practice

Pehle khud, phir neeche kholo.

12345 678910

P1

P=2000, SI=400, T=4. R?

  1. 5%
  2. 20%
  3. 8%
  4. 2%

Solution

  1. 40000/8000

    5%.

Answer5%
P2

P=1500, R=10%, SI=300. T?

  1. 2 yr
  2. 3 yr
  3. 5 yr
  4. 20 yr

Solution

  1. 30000/15000

    2.

Answer2 yr
P3

2000, 10%, 73 days (365). SI?

  1. 40
  2. 200
  3. 73
  4. 146

Solution

  1. T=1/5

    40.

Answer40
P4

3 yr SI=450. 5 yr SI?

  1. 750
  2. 450
  3. 900
  4. 150

Solution

  1. ∝ t

    750. CI nahi.

Answer750
P5

5000, 12%, 2.5 yr. SI?

  1. 1500
  2. 1200
  3. 600
  4. 1875

Solution

  1. 5000×30/100

    1500.

Answer1500
P6

15 saal, 4-guna. R?

  1. 20%
  2. 15%
  3. 26⅔%
  4. 4%

Solution

  1. 300/15

    20%. C 400/15 mix.

Answer20%
P7

2400, 12%, 3 yr. SI?

  1. 864
  2. 720
  3. 288
  4. 960

Solution

  1. 2400×36/100

    864.

Answer864
P8

10% phir 20% discount. Is chapter?

  1. Nahi — Profit / loss
  2. Haan, SI 28
  3. R=30%
  4. T=2

Solution

  1. Off

    A. Net 28% wahan.

AnswerA
P9

Year-2 interest on 1100. Is chapter?

  1. Nahi — Compound interest
  2. Haan, SI 100
  3. PRT
  4. Double

Solution

  1. On interest

    A. Yahan har saal 100 (P pe).

AnswerA
P10

Profit share capital × time. Is chapter?

  1. Nahi — Partnership
  2. Haan, PRT
  3. SI split
  4. Ratio 8:12:15

Solution

  1. Share

    A. T yahan interest-time, partner-time wahan.

AnswerA

← Index · Profit / loss · Percentage

Agle topic: Compound interest.