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Answers
Answer:
12) (c) 195°
13) (a) 59⁷/₁₂ min past 3
14) (a) 32⁸/₁₂ mins
Step-by-step explanation:
12) A clock consists of places 1 - 12. Since it is circular, we can consider that while going from 12 to 12, a hand covers 360°, i.e. while going from any number to the next number, a hand covers 360÷12 = 30°.
At 10:25, the hour hand is between 10 and 11 and the minute hand is at 5. The angle between 11 and 5 is 30×6=180° and since the hour hand is between 10 and 12, we have to add half the angle between 10 and 11, i.e. 15°
=> the angle subtended by the hour and minute hand = 195°
since 195° is reflex, (c) is the answer.
13) The watch gains 5s in 3mins and was set right at 7am.
It is showing quarter past 4 in the watch, i.e. 4:15pm.
=> 9hrs 15mins have passed in the watch
=> 9×60+15 = 555mins have passed
since the watch gains 5s in 3mins, in 555mins it gains 555÷3×5 = 185×5 = 925s have passed
925s = 925/60 = 15⁵/₁₂ mins
thus, 15⁵/₁₂ extra time has passed
=> real time is 15⁵/₁₂mins before 4:15pm
=> real time = 3:59⁷/₁₂ = 59⁷/₁₂ mins past 3 = (a)
14) The hands of a clock coincide 22 times a day.
=> in this clock, the total duration of a day = 64×22 = 1408mins
but a day has 24×60 = 1440 mins
therefore it has 1440-1408 = 32 mins less
32 mins is an approximation, so the answer might be closest one, i.e. (a)