Exercise 2.4 — More Applications

Exercise 2.4 — More Applications

Exercise 2.4 presents a second set of application problems with greater complexity than Exercise 2.2 — involving multiple relationships between unknowns, ratio conditions, and consecutive number problems. This exercise in Class 8 Mathematics prepares you for the higher-difficulty word problems in board examinations.

Advanced Problem-Solving Techniques

• For ratio problems: if x:y = a:b, express x = ak and y = bk then use the given condition to find k.
• For consecutive integer problems: use n, n+1, n+2 for consecutive integers; 2n, 2n+2, 2n+4 for consecutive evens.
• For perimeter problems: write the perimeter formula first, substitute the relationship given, then solve.
• For problems with two unknowns where only one is asked, express the second in terms of the first and eliminate.
• Check that the solution is meaningful in context — negative ages or fractional people indicate a setup error.

Connecting to Higher Classes

The problem-solving framework in Exercise 2.4 carries directly into simultaneous equations (Class 9) and quadratic word problems (Class 10). Every technique practised here — defining variables, forming equations, checking solutions in context — will be used repeatedly throughout your mathematics education.

How to Use This Lesson

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