Word Problems Application — Study Notes

Overview

Word problems are the bridge between classroom mathematics and real-world scenarios. In SOF IMO, these problems test whether you can read a situation, translate it into mathematical language, solve it using the correct formulas or methods, and interpret the answer back in context. They typically appear in both the Everyday Mathematics section and the Achievers Section.

Expect problems drawn from percentage, profit-loss, time-speed-distance, ratios, linear equations, geometry (areas, perimeters), mensuration (volumes, surface areas), statistics, and number theory. The key skill is **problem comprehension**: identifying what is given, what is asked, and which mathematical operation or formula applies. Most students lose marks not because they can't do the math, but because they misread the question or set up the equation incorrectly.

Mastering word problems requires practice in recognizing common patterns (age problems, mixture problems, train problems), translating words into algebraic expressions, and always checking if your numerical answer makes practical sense. A negative age or a speed of 500 km/h for a bicycle should immediately signal an error.

Key Concepts

• **Read twice, solve once**: Read the entire problem carefully before writing anything. Identify the unknown quantity you need to find and label it clearly (often as *x* or another variable).

• **Unit consistency**: All quantities in a calculation must use the same units. Convert hours to minutes, kilometers to meters, or rupees to paise before applying formulas.

• **Translate phrases into math**: "5 more than a number" → x + 5; "twice the sum of two numbers" → 2(x + y); "A is 20% less than B" → A = 0.8B.

• **Draw diagrams where possible**: For geometry, distance-time, and mixture problems, a simple sketch or number line clarifies relationships and prevents errors.

• **Check reasonableness**: After computing, ask: Does this answer fit the story? If a man's age comes out as 150 years or a discount exceeds 100%, revisit your setup.

• **Work backwards for verification**: Substitute your answer back into the original conditions to confirm it satisfies all the given constraints.

Formulas / Key Facts

1. **Percentage**: Part = (Percentage/100) × Whole; Increase = Original × (1 + r/100); Decrease = Original × (1 − r/100).

2. **Profit and Loss**: Profit = Selling Price − Cost Price; Profit% = (Profit/CP) × 100; Loss% = (Loss/CP) × 100.

3. **Discount**: Discount = Marked Price − Selling Price; Discount% = (Discount/MP) × 100; SP = MP × (1 − Discount%/100).