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    Question

    Manoj can complete a job in 10 days which Rakesh can do

    in 15 days. Rakesh can finish a task in 20 days which Suresh can complete in 25 days. In how many days Suresh and Rakesh together can finish the work that Manoj can do in 90 days?
    A 45 days Correct Answer Incorrect Answer
    B 75 days Correct Answer Incorrect Answer
    C 65 days Correct Answer Incorrect Answer
    D 20 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the efficiency of Manoj, Rakesh, and Suresh be p, q, and r units/day respectively. So, 10p = 15q p = 15q / 10 p = 3q / 2 Again, 20q = 25r r = 20q / 25 r = 4q / 5 Now, ratio of efficiencies of Manoj, Rakesh, and Suresh = (3q/2) : q : (4q/5) Multiply each term by 10 to remove fractions = (15q) : (10q) : (8q) ⇒ 15 : 10 : 8 Let p = 15e, q = 10e, and r = 8e Let required time = T days So, (10e + 8e) × T = 15e × 90 ⇒ 18T = 1350 ⇒ T = 75 days

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