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    Question

    ‘P’ and ‘Q’ together can complete an analysis in

    40 days, while ‘Q’ and ‘R’ together can complete the same analysis in 30 days. ‘P’ and ‘Q’ together worked on it for 35 days and then ‘R’ alone completed the remaining work in 5 days. If ‘P’, ‘Q’, and ‘R’ started the analysis and worked together till its completion for which they received Rs. 1200 as total wage, then the share of ‘P’ out of the total wage will be: 
    A Rs 800 Correct Answer Incorrect Answer
    B Rs 600 Correct Answer Incorrect Answer
    C Rs 700 Correct Answer Incorrect Answer
    D Rs 400 Correct Answer Incorrect Answer
    E Rs 500 Correct Answer Incorrect Answer

    Solution

    Let the total amount of work = 120 units (LCM of 40 and 30) Work done by ‘P’ and ‘Q’ together in one day = 120 / 40 = 3 units Work done by ‘Q’ and ‘R’ together in one day = 120 / 30 = 4 units Work done by ‘P’ and ‘Q’ together in 35 days = 35 × 3 = 105 units Remaining work = 120 - 105 = 15 units Efficiency of ‘R’ = 15 / 5 = 3 units per day Efficiency of ‘Q’ = 4 - 3 = 1 unit per day Efficiency of ‘P’ = 3 – 1 = 2 units per day Share of ‘P’ = (2 / (2 + 1 + 3)) × 1000 = 2/6 × 1200 = Rs 400

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