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    Question

    P and Q can do a piece of work in 32 and 40 days

    respectively. They began to work together but P leaves after sometimes and Q completed remaining work in 16 days. After how many days did P leaves (in days)?
    A 32/5 Correct Answer Incorrect Answer
    B 31/3 Correct Answer Incorrect Answer
    C 32/3 Correct Answer Incorrect Answer
    D 80/3 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let P worked for x days According to question ⇒ `x/32+(x+16)/40` = 1 ⇒ `(5x+4(x+16))/160` = 1 ⇒ 5 x + 4x + 64 = 160 ⇒ 9x = 160 – 64 = 96 ⇒ `x=96/9=32/3 days P left the work after 32/3 days. Alternate Method; P Q 32 40 LCM = 160 units 5 : 4 For last 16 days, Q alone completed = 4 x 16 = 64 units So remaining is done by both = (160 -64)/(5+4) = 96/9 = 32/3 days Hence P left after 32/3 days.

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