A man performs (2)/(15) of the total journey by rail, (9)/(20) by tonga and the remaining 10 km

Step 1: Let the total journey be denoted as ( x ) km. Step 2: According to the problem, the man

A man performs (2)/(15) of the total journey by rail,...

A man performs $\frac{2}{15}$ of the total journey by rail, $\frac{9}{20}$ by tonga and the remaining $10 \mathrm{~km}$ on foot. The total journey is :
(a) $15.6 \mathrm{~km}$
(b) $12.8 \mathrm{~km}$
(c) $16.4 \mathrm{~km}$
(d) $24 \mathrm{~km}$a

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Key Concepts

Fractional Parts of a Whole

This concept involves expressing portions of a total quantity as fractions. In many real-world problems, especially in journeys or mixture problems, parts are represented as fractions, and the sum of these parts along with any fixed amounts equals the whole. Understanding how to interpret and manipulate fractional parts is essential for breaking down the overall problem into manageable segments.

Algebraic Equation Formation

Algebraic equation formation is the process of translating a word problem into a mathematical equation. It involves defining variables for unknown quantities and setting up equations by combining fractional parts, fixed amounts, or other operations. This method is fundamental in solving problems systematically, ensuring that each element described in the scenario is accurately represented mathematically.

Solving Linear Equations Involving Fractions

Solving linear equations that include fractions requires techniques such as finding a common denominator and performing operations to isolate the variable. This is crucial in problems where parts of a total are represented by fractions, as it allows for the summing of terms and the elimination of fractional components to determine the unknown total. Mastery of this concept enables accurate and efficient resolution of varied algebraic challenges.

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