1. Question:At what time between 5 and 6 o'clock are the hands of a 3 minute apart ? 

    Answer
    At 5 o'clock, the minute hand is 25 min. space behind the hour hand.
    
    Case I: Minute hand is 3 min.spaces behind the hour hand.
    
    In this case, the minute hand has to gain (25 - 3) = 22 minute space 
    
    55 min are gained in 60 min.
    
    22 min. are gained in` (60/55 xx 22)` min. = 24 min
    
    :. The hands will be 3 min. apart at` 31 5/11` min. past 5.
    
    Case II : Minute hand is 3 min.spaces ahead of the hour hand.
    
    In this case, the minute hand has to gain (25 + 3) = 28 minute spaces.
    
    55 min.are gained in 60 min.
    
    28 min. are gained in` (60/55 xx 28)` `= 31 5/11` min.
    
    :. The hands will be 3 min. apart at `31 5/11` min. past 5.






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  2. Question:A watch which gains uniformly's is 5 min. slow at 8 o'clock in the morning on Sunday and it is 5 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct ? 

    Answer
    Time from 8 a.m. on Sunday to 8 p.m. on following Sunday
    
           = 7 days 12 hours = 180 hours.
    
    :. The watch gains `(5 + 5 4/5)` min or `54/5` min. in 180 hrs.
    
    Now` 54/5` min. are gained in 180 hrs.
    
    :. 5 min. are gained in `(180 xx 5/54 xx 5)` hrs.
    
    = 83 hrs 20 min. = 3 days 11 hrs 20 min.
    
    :. watch is correct 3 days 11 hrs 20 min. past 7 p.m.on Wednesday.
    
    :. It will be correct at 20 min.past 7 p.m. on Wednesday.






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  3. Question:A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4 th day ? 

    Answer
    Time from 5 a.m. on 4th day = 89 hours.
    
    Now 23 hrs 44 min. of this clock = 24 hours of correct clock.
    
    `:. 356/15` hrs of this clock = 24 hours of correct clock.
    
    89 hrs of this clock` = (24 xx 15/356 xx 89)` hrs hours of correct clock.
    
       = 90 hrs of correct clock.
    
    So, the correct time is 11 p.m.






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  4. Question:A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day ? 

    Answer
    Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hrs.
    
    24 hours 10 min.of this clock = 24 hours of the correct clock.
    
    `145/6` hrs of this clock = 24 hrs of the correct clock
    
    29 hrs of this clock` = (24 xx 6/145 xx 29)` hrs of the correct clock
    
       = 28 hrs 48 min of correct clock
    
    :. The correct time is 28 hrs 48 min. after 8 a.m.
    
    This is 48 min. past 12.






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  5. Question:Find the cash required to purchase `Rs.3200,7 1/2%` stock at 107 `(brokerage 1/2%)` 

    Answer
    Cash required to purchase Rs. 100 stock
    
    ` = Rs.(107 + 1/2) = Rs.215/2.`
    
     Cash required to purchase Rs. 3200 stock
    
     ` = Rs. (215/2 xx 1/100 xx 3200)`
    
      `= Rs. 3440.`






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