24. After 9 O'clock a 9 pm and 10 p...
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24. After 9 O'clock a 9 pm and 10 pm will the ter 9 o'clock at what time between 9 pm and 10 pm hour and minute hands of a clock point in opposite directions ? (1) 15 min past 9 (2) 16 min past 9 (3) 16 min past 9 (4) 17min past 9 11 no

11th - 12th Class
Maths
Solution
223
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24. (3) At 9 o' clock, the min hand is ( 9 times 5=45 ) min spaces behind the hour hand. Therefore, the minute hand will have to gain ( 45-30=15 ) min spaces over the hour hand. ( therefore ) Gain of 55 min spaces equals 60 min. ( therefore ) Gain of 15 min spaces equals [ =frac{60}{55} times 15=frac{180}{11}=16 frac{4}{11} ] Therefore, hour and minute hands of a clock point in opposite directions after ( 9 mathrm{O}^{prime} ) clock at ( 16 frac{4}{11} ) min past 9
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