Class 11 Maths and Statistics Part 2 Chapter 9: Commercial Mathematics

Key concepts: Commercial Mathematics

Percentage

Per cent means per hundred. Percentage increase (decrease) = increase (decrease)/original × 100. To increase a number by x%, multiply by (100 + x)/100; to decrease, by (100 − x)/100.

Profit and loss

Gain = S.P. − C.P.; Loss = C.P. − S.P. Gain% and loss% are always calculated on C.P. S.P. = C.P. × (100 + gain%)/100. A seller using a false weight gains error/(true value − error) × 100 %.

Simple interest

I = PNR/100 and amount A = P + I, where P is the principal, N the period in years and R the rate per cent per annum.

Compound interest

A = P(1 + R/100)ᴺ and C.I. = A − P. For half-yearly compounding use R/2 and 2N.

Depreciation

The fall in value of an asset. Under the reducing balance method, value after N years = P(1 − R/100)ᴺ.

Partnership

Profit is shared in the ratio of capitals invested; if the periods differ, in the ratio of capital × time.

GST

Goods and Services Tax on supply of goods and services. Intra-state supply: CGST + SGST (each half the rate). Inter-state supply: IGST. Input tax credit lets a dealer set off GST paid on purchases against GST collected on sales.

Shares and dividends

Face value (nominal value) stays fixed; market value changes. A share above face value is at a premium, below at a discount. Dividend is always paid on face value. Rate of return = annual dividend/market value × 100.

Quick revision: important points

• If a price rises by x%, consumption must fall by x/(100 + x) × 100 % to keep expenditure the same.
• If A's income is r% more than B's, B's income is r/(100 + r) × 100 % less than A's.
• Selling two items at x% gain and x% loss gives an overall loss of x²/100 %.
• C.I. for 2 years − S.I. for 2 years = P(R/100)².
• Number of shares = investment/market value; income = number of shares × dividend per share.

Practice MCQs with answers

1. 20% of 50 is:

   1. 5
   2. 10
   3. 20
   4. 25
   Show answer

   Answer: B. 10
   20/100 × 50 = 10.

2. If a price rises from ₹200 to ₹250, the percentage increase is:

   1. 20%
   2. 25%
   3. 50%
   4. 12.5%
   Show answer

   Answer: B. 25%
   50/200 × 100 = 25%.

3. If C.P. = ₹3,800 and S.P. = ₹4,560, the profit per cent is:

   1. 16.67%
   2. 20%
   3. 25%
   4. 18%
   Show answer

   Answer: B. 20%
   760/3800 × 100 = 20%.

4. An article sold for ₹5,250 at a loss of 25% cost:

   1. ₹6,562.50
   2. ₹7,000
   3. ₹6,000
   4. ₹4,200
   Show answer

   Answer: B. ₹7,000
   C.P. = 5250 × 100/75 = 7000.

5. The simple interest on ₹5,000 at 8% p.a. for 3 years is:

   1. ₹400
   2. ₹1,200
   3. ₹1,000
   4. ₹1,500
   Show answer

   Answer: B. ₹1,200
   5000 × 3 × 8/100 = 1200.

All Class 11 Maths and Statistics chapters

• Part 1 Chapter 1: Sets and Relations
• Part 1 Chapter 2: Functions
• Part 1 Chapter 3: Complex Numbers
• Part 1 Chapter 4: Sequences and Series
• Part 1 Chapter 5: Locus and Straight Line
• Part 1 Chapter 6: Determinants
• Part 1 Chapter 7: Limits
• Part 1 Chapter 8: Continuity
• Part 1 Chapter 9: Differentiation
• Part 2 Chapter 1: Partition Values
• Part 2 Chapter 2: Measures of Dispersion
• Part 2 Chapter 3: Skewness
• Part 2 Chapter 4: Bivariate Frequency Distribution
• Part 2 Chapter 5: Correlation
• Part 2 Chapter 6: Permutations and Combinations
• Part 2 Chapter 7: Probability
• Part 2 Chapter 8: Linear Inequations
• Part 2 Chapter 9: Commercial Mathematics

Class 11 Maths and Statistics notes: all chapters