Profit, Loss and Simple Interest
1. Basic Terminology
Key Terms
| Term | Meaning |
|---|---|
| Cost Price (CP) | The price at which an article is PURCHASED |
| Selling Price (SP) | The price at which an article is SOLD |
| Profit | SP > CP. Profit = SP - CP |
| Loss | CP > SP. Loss = CP - SP |
| Overhead Charges | Additional costs (transport, repairs). Added to CP. |
Profit and Loss Formulas
- Profit % = (Profit / CP) × 100%
- Loss % = (Loss / CP) × 100%
Important
Profit% and Loss% are ALWAYS calculated on COST PRICE (unless stated otherwise).
2. Finding SP Given CP and Profit/Loss %
When Profit% is Given
SP = CP × (100 + Profit%) / 100
Example: 'If CP = ₹500 and Profit% = 12%, find SP.' SP = 500 × (100 + 12)/100 = 500 × 112/100 = 5 × 112 = ₹560.
When Loss% is Given
SP = CP × (100 - Loss%) / 100
Example: 'If CP = ₹800 and Loss% = 10%, find SP.' SP = 800 × (100 - 10)/100 = 800 × 90/100 = 8 × 90 = ₹720.
3. Finding CP Given SP and Profit/Loss %
When Profit% is Given
CP = SP × 100 / (100 + Profit%)
Example (ICSE 2024, 3 marks): 'By selling a chair for ₹720, a man gains 20%. Find the cost price.' CP = 720 × 100 / (100 + 20) = 720 × 100/120 = 720 × 5/6 = ₹600.
When Loss% is Given
CP = SP × 100 / (100 - Loss%)
Example: 'By selling a watch for ₹450, a man loses 10%. Find the CP.' CP = 450 × 100 / (100 - 10) = 450 × 100/90 = 450 × 10/9 = ₹500.
4. Discount
Marked Price (MP) or List Price: The price marked on the article. Discount: Reduction offered on the marked price.
Formulas
- Discount = MP - SP
- Discount % = (Discount / MP) × 100%
- SP = MP × (100 - Discount%) / 100
Worked Example (ICSE 2023, 3 marks)
'A shopkeeper marks a shirt at ₹800 and offers a 15% discount. Find the selling price.' Discount = 15% of 800 = (15/100) × 800 = ₹120. SP = 800 - 120 = ₹680. OR directly: SP = 800 × (100 - 15)/100 = 800 × 85/100 = ₹680.
Successive Discounts
Two discounts offered one after another. Example: 'A 10% discount followed by another 5% discount on ₹2,000.' After first discount: SP₁ = 2,000 × 90/100 = ₹1,800. After second discount: SP₂ = 1,800 × 95/100 = ₹1,710.
5. Simple Interest
SIMPLE INTEREST is the interest calculated on the ORIGINAL principal for the entire period.
Formula
SI = (P × R × T) / 100
Where:
- P = Principal (the amount borrowed or invested)
- R = Rate of interest per annum (per year)
- T = Time in years
- SI = Simple Interest
- Amount (A) = P + SI
Worked Example (ICSE 2024, 3 marks)
'Find Simple Interest on ₹2,000 for 3 years at 8% per annum.' SI = (2,000 × 8 × 3) / 100 = 2,000 × 24 / 100 = ₹480. Amount = 2,000 + 480 = ₹2,480.
Finding Principal, Rate, or Time
- P = (SI × 100) / (R × T)
- R = (SI × 100) / (P × T)
- T = (SI × 100) / (P × R)
Example (ICSE 2023, 3 marks)
'At what rate% will ₹1,200 earn ₹240 as simple interest in 4 years?' R = (240 × 100) / (1,200 × 4) = 24,000 / 4,800 = 5% per annum.
6. Combined Problems (ICSE Focus)
Example: Profit then Discount
'A trader buys goods for ₹1,000. He marks them at 20% above CP and gives a 10% discount. Find his profit percentage.' MP = 1,000 × (120/100) = ₹1,200. SP = 1,200 × (90/100) = ₹1,080. Profit = 1,080 - 1,000 = ₹80. Profit% = (80/1,000) × 100% = 8%.
Common Mistake
'Calculating profit% on SP instead of CP.' Wrong: Profit% = (80/1080) × 100 = 7.4%. Right: Profit% = (80/1000) × 100 = 8%.
7. ICSE Exam Focus
| Topic | Marks | Frequency |
|---|---|---|
| Finding SP or CP from profit/loss% | 2-3 marks | Very High |
| Discount problems | 3 marks | High |
| Simple Interest (all variations) | 3-4 marks | Very High |
| Combined profit + discount | 4 marks | Medium |
Common Mistakes in ICSE Exams
- Calculating profit% on SELLING PRICE instead of cost price.
- Forgetting to convert time to years in simple interest (T in months must be T/12).
- Discount always calculated on MARKED PRICE, not on CP.
- Forgetting overhead charges when calculating effective CP.
Self-Test (5 Questions)
Q1. If CP = ₹400 and Profit% = 15%, find SP. (2 marks)
- A) ₹440
- B) ₹450
- C) ₹460
- D) ₹470
Q2. 'A table bought for ₹1,200 is sold at a loss of 8%. Find the selling price.' (2 marks)
Q3. 'A book is marked at ₹500 and sold at ₹425. Find the discount percentage.' (2 marks)
Q4. 'Find Simple Interest on ₹3,600 for 2 years at 5% per annum.' (2 marks)
Q5. 'At what rate% will ₹2,500 amount to ₹3,000 in 4 years?' (3 marks)
Answers
A1. C) ₹460. (SP = 400 × 115/100 = ₹460.) A2. ₹1,104. (SP = 1,200 × 92/100 = ₹1,104.) A3. 15%. (Discount = 75. % = 75/500 × 100 = 15%.) A4. ₹360. (SI = 3,600 × 5 × 2 / 100 = ₹360.) A5. 5% p.a. (SI = 3000 - 2500 = 500. R = 500 × 100 / (2500 × 4) = 5%.)
