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SSC GD 2025 PYQ — Question 54

SSC GD Const 2025 (English) - 06 Feb 2025 - Shift 3 • Quantitative Aptitude • Q54

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X can complete a task in 15 days, and Y can complete the same task in 20 days. If X and Y work on alternate days, starting with X, in how many days will the work be completed?

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Correct answer: B

Explanation

X’s 1 day work=115Y’s 1 day work=1202 days’ work=115+120=76016 days’ work=8×760=1415Remaining work=1−1415=11517th day=X completes 115 work∴ Total time=17 days \begin{aligned} \text{X's 1 day work} &= \frac{1}{15} \\ \text{Y's 1 day work} &= \frac{1}{20} \\[4pt] \text{2 days' work} &= \frac{1}{15}+\frac{1}{20}=\frac{7}{60} \\[4pt] \text{16 days' work} &= 8\times\frac{7}{60}=\frac{14}{15} \\[4pt] \text{Remaining work} &= 1-\frac{14}{15}=\frac{1}{15} \\[4pt] \text{17th day} &= X \text{ completes } \frac{1}{15} \text{ work} \\[4pt] \therefore\ \text{Total time} &= 17\ \text{days} \end{aligned}