A can lay a railway track between two given stations in 8 days and B can do the same job in 24 days. With the help of C, they can do the job in 3 days. C alone can do the job in:

7 days

8 days

6 days

9 days

APEDIA

NTPC Graduate Tier 1

2025 • 09 Jun, 2025 • Shift-1

A can lay a railway track between two given stations in 8 days and B can do the same job in 24 days. With the help of C, they can do the job in 3 days. C alone can do the job in:

Correct Answer

6 days

Rate of Work Formulation: In time and work matrices, an individual's efficiency is mathematically evaluated as the reciprocal of their completion time. A's dail......

💡 Analysis & Explanation

Rate of Work Formulation ▼

In time and work matrices, an individual's efficiency is mathematically evaluated as the reciprocal of their completion time. A's daily independent work rate is 1/8. B's daily independent work rate is 1/24.

Combined Efficiency Evaluation ▼

When working as a highly synchronized team (A + B + C), they finish the entire task in exactly 3 days. Therefore, their collective daily work rate is exactly 1/3.

Variable Isolation (Finding C) ▼

The collective equation is formed as: (1/8) + (1/24) + (1/C) = (1/3). We must align the denominators to strictly isolate C. Creating a common denominator of 24, we convert the equation: (3/24) + (1/24) + (1/C) = (8/24).

Final Mathematical Derivation ▼

Combining the known fractions gives (4/24) + (1/C) = (8/24). By shifting terms, we deduce 1/C = (8/24) - (4/24) = 4/24. Simplifying this fraction drastically leaves 1/6. By reciprocating, C's total time is revealed.

Conclusion ▼

Worker C, operating entirely independently, requires exactly 6 days.

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A can lay a railway track between two given stations in 8 days and B can do the same job in 24 days. With the help of C, they can do the job in 3 days. C alone can do the job in: