Helper joins mid-way on a construction task A mason can build a tank in 12 hours. He works alone for 6 hours, then a boy helps and they finish the job in 5 more hours. How long would the boy take to complete the entire job alone?

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:When a helper joins partway, compute the initial portion done by the first worker, then infer the combined rate to deduce the helper’s individual rate. Given Data / Assumptions: Mason completes job in 12 h ⇒ rate = 1/12 per hour. Mason works alone for 6 h ⇒ completes 1/2 of the job. Remaining 1/2 is done by mason + boy in 5 h. Concept / Approach:Combined rate = remaining work / time. Boy’s rate = combined rate − mason’s rate. Time for boy alone = 1 / boy’s rate. Step-by-Step Solution: Work after 6 h alone = 6 * (1/12) = 1/2Remaining work = 1/2Combined rate (mason + boy) = (1/2) / 5 = 1/10 per hourMason’s rate = 1/12 ⇒ Boy’s rate = 1/10 − 1/12 = 1/60 per hourBoy alone time = 1 / (1/60) = 60 h Verification / Alternative check:In 5 hours together they do 5 * (1/10) = 1/2, which matches the remaining half. Why Other Options Are Wrong:45 h, 30 h, 64 h do not match the inferred boy’s rate 1/60. Common Pitfalls:Assuming linear sharing without first computing combined rate from the second phase. Final Answer:60 h

Helper joins mid-way on a construction task A mason can build a tank in 12 hours. He works alone for 6 hours, then a boy helps and they finish the job in 5 more hours. How long would the boy take to complete the entire job alone?

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