A person covers 2/15 of a journey by rail, 9/20 by tonga, and the remaining 10 km on foot. What is the total length of the journey?
Aptitude
Time and Distance
Difficulty: Easy
Choose an option
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A15.6 km
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B12.8 km
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C16.4 km
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D24 km
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E20 km
Answer
Correct Answer: 24 km
Explanation
Introduction / Context:Journeys expressed in fractional parts can be reconstructed by summing known fractions and tying the leftover fraction to a given absolute remainder.
Given Data / Assumptions:
- By rail = 2/15 of total D.
- By tonga = 9/20 of D.
- On foot = 10 km = remaining fraction of D.
Concept / Approach:Compute remaining fraction: 1 - (2/15 + 9/20). Set that fraction equal to 10/D and solve for D.
Step-by-Step Solution:
2/15 + 9/20 = 8/60 + 27/60 = 35/60 = 7/12Remaining fraction = 1 - 7/12 = 5/125/12 of D = 10 km → D = 10 * (12/5) = 24 kmVerification / Alternative check:Check parts: Rail = 2/15 * 24 = 3.2 km; Tonga = 9/20 * 24 = 10.8 km; Remaining = 10 km; total = 24 km.
Why Other Options Are Wrong:They result from arithmetic errors in fraction addition or inversion.
Common Pitfalls:Failing to use common denominators when adding fractions; forgetting to equate the leftover fraction to 10/D.
Final Answer:24 km