Ratio, Proportion, Percentages and Averages (Business Applications) Questions

Question 1

Define ratio.

Accepted Answer

Ratio is a comparison of two like quantities expressed as a:b.

Question 2

What is percentage?

Accepted Answer

Percentage means “per hundred” and is written as x% = x/100.

Question 3

State the condition of proportion.

Accepted Answer

If a:b = c:d, then a×d = b×c.

Question 4

What is weighted mean?

Accepted Answer

Weighted mean is an average computed using Σ(wx)/Σw.

Question 5

Calculate net discount for successive discounts of 20% and 10%.

Accepted Answer

Net discount = 20 + 10 − (20×10)/100 = 28%.

Question 6

If 25% of N is 80, find N.

Accepted Answer

N = 80 × 100/25 = 320.

Question 7

Explain direct and inverse proportion with one example each.

Accepted Answer

**Direct proportion (direct variation):**
Two quantities are in direct proportion when they change in the **same direction**.
- y ∝ x  ⇒  y = kx (k is constant)
So, if x increases, y increases in the same ratio.

**Example (business):** If sales are proportional to advertising (other things constant), then increasing advertising from 10 units to 15 units changes sales by the factor 15/10.

**Inverse proportion (inverse variation):**
Two quantities are in inverse proportion when one increases and the other decreases such that their **product remains constant**.
- y ∝ 1/x  ⇒  y = k/x

**Example (work-time):** 12 workers finish a job in 10 days.
Days for 15 workers = 10 × (12/15) = 8 days (same efficiency).

Question 8

Define percentage change and illustrate with an example.

Accepted Answer

**Percentage change** shows how much a value has increased or decreased **relative to the old value**.

**Formula:**
% change = ((New − Old) / Old) × 100

- Positive result → **% increase**
- Negative result → **% decrease**

**Example:** Value changes from 500 to 650.
Increase = 650 − 500 = 150
% increase = (150/500) × 100 = 30%

So, the value increases by **30%**.

Question 9

Compute weighted mean price for ₹10 (100 units) and ₹12 (50 units).

Accepted Answer

**Weighted mean** is used when values have different quantities/importance.

**Formula:**
Weighted mean = Σ(wx) / Σw

Here, x = price and w = quantity.
Weighted mean = (100×10 + 50×12) / (100 + 50)
= (1000 + 600) / 150
= 1600 / 150
= 10.67 (approx.)

So, the weighted mean (average) price is **₹10.67 (approx.)** per unit.

Question 10

A sum of ₹1800 is divided in the ratio 2:3:4. Find each share.

Accepted Answer

To divide ₹1800 in the ratio 2:3:4:

**Step 1: Total parts**
2 + 3 + 4 = 9

**Step 2: Shares**
- First = (2/9) × 1800 = ₹400
- Second = (3/9) × 1800 = ₹600
- Third = (4/9) × 1800 = ₹800

So, the shares are **₹400, ₹600 and ₹800**.

Question 11

Two successive price changes are +20% and −10%. Find the net percentage change.

Accepted Answer

Successive percentage changes are applied **one after another**.

Let the original price be 100.
- After +20%: 100 × 1.20 = 120
- After −10%: 120 × 0.90 = 108

Net change = 108 − 100 = +8
So, net percentage change = **8% increase**.

(Shortcut: net % = a + b + (a×b)/100 = 20 + (−10) + (20×−10)/100 = 8.)

Question 12

12 workers finish a job in 10 days. How many days will 15 workers take?

Accepted Answer

This is an **inverse proportion** situation (workers × days = constant).

Work = 12 × 10 = 120 worker-days.
Days for 15 workers = 120/15 = 8 days.

So, **15 workers will take 8 days** (assuming same efficiency).

Question 13

Define ratio and proportion. Explain their importance in business calculations with examples.

Accepted Answer

### Ratio
A **ratio** is a comparison of two like quantities expressed as a:b.
Example: Profit ₹20,000 and sales ₹1,00,000 ⇒ profit:sales = 20,000:1,00,000 = 1:5.

### Proportion
A **proportion** is an equality of two ratios.
If a:b = c:d, then **a×d = b×c**.

### Importance in business calculations (any 4–5 points)
- **Allocation and distribution:** Divide salary/bonus/budget among departments or partners in a fixed ratio.
- **Costing and production planning:** Maintain raw material mix in a required ratio (e.g., 2:3 blend).
- **Financial and performance analysis:** Ratios like current ratio, gross profit ratio, debt–equity help decision-making.
- **Sales targets and scaling:** Use proportion to scale targets when working days/sales force/output changes.
- **Trade calculations:** Many discount, markup, commission and tax problems use proportional reasoning.

**Conclusion:** Ratio and proportion give a simple, accurate way to compare quantities and make business decisions using numbers.

Question 14

Explain percentages and successive discounts. Solve: MP ₹2000, discount 20% and then 10%. Find SP.

Accepted Answer

### Percentages
Percentage means “per hundred” and is written as x% = x/100. It is used in business for **discounts, commission, taxes, profit rates and growth rates**.

### Successive discounts
When two discounts are given one after another, the second discount is applied on the **reduced price**.
So we multiply the remaining factors.

### Problem
MP = ₹2000

After 20% discount:
SP1 = 2000 × (1 − 20/100) = 2000 × 0.80 = ₹1600

After 10% discount on ₹1600:
Final SP = 1600 × (1 − 10/100) = 1600 × 0.90 = ₹1440

**Answer:** Selling price = **₹1440**.

(Shortcut: net discount = 20 + 10 − (20×10)/100 = 28%; 28% of 2000 = 560; 2000 − 560 = 1440.)

Question 15

Explain arithmetic mean and weighted mean. Why is weighted mean more useful in business? Give an example.

Accepted Answer

### Arithmetic mean
Arithmetic mean is the simple average where all observations are treated equally.
Mean = Σx / n

### Weighted mean
Weighted mean gives different importance (weights) to values.
Weighted mean = Σ(wx) / Σw

### Why weighted mean is more useful in business
In business, values usually come with **quantities/importance**, so a simple mean can be misleading. Weighted mean is used for:
- Average selling price when quantities sold differ
- Average marks with different credits
- Average wage rate when hours differ
- Average cost when output differs

### Example (average price)
100 units at ₹10 and 50 units at ₹12:
Weighted mean = (100×10 + 50×12) / (100 + 50)
= 1600/150 = 10.67 (approx.)

Simple mean of prices would be (10 + 12)/2 = 11, which ignores quantities.

**Conclusion:** Weighted mean gives the correct business average because it considers volume/importance.

Ratio, Proportion, Percentages and Averages (Business Applications)

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