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    Question

    β€˜P’ and β€˜Q’ together can complete an analysis in

    40 days, while β€˜Q’ and β€˜R’ together can complete the same analysis in 30 days. β€˜P’ and β€˜Q’ together worked on it for 35 days and then β€˜R’ alone completed the remaining work in 5 days. If β€˜P’, β€˜Q’, and β€˜R’ started the analysis and worked together till its completion for which they received Rs. 1200 as total wage, then the share of β€˜P’ out of the total wage will be:Β 
    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 β€˜P’ and β€˜Q’ together in one day = 120 / 40 = 3 units Work done by β€˜Q’ and β€˜R’ together in one day = 120 / 30 = 4 units Work done by β€˜P’ and β€˜Q’ together in 35 days = 35 Γ— 3 = 105 units Remaining work = 120 - 105 = 15 units Efficiency of β€˜R’ = 15 / 5 = 3 units per day Efficiency of β€˜Q’ = 4 - 3 = 1 unit per day Efficiency of β€˜P’ = 3 – 1 = 2 units per day Share of β€˜P’ = (2 / (2 + 1 + 3)) Γ— 1000 = 2/6 Γ— 1200 = Rs 400

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