type 4 time gained or lost by clock Practice Questions Answers Test with Solutions & More Shortcuts
clocks PRACTICE TEST [5 - EXERCISES]
type 1 angle between the hands of clock
type 2 position of hands of the clock
type 3 faulty clock
type 4 time gained or lost by clock
type 5 comparing clocks
Question : 1
The minute hand of a clock overtakes the hour hand at intervals of 76 min of the correct time. How much does a clock gain or lose in a day ?
a) 198 $169/209$ min (loss)
b) 198 $169/209$ min (gain)
c) 199 $169/209$ min (loss)
d) 199 $169/209$ min (gain)
Answer »Answer: (c)
Therefore, required result = $(720/11 - x) (60 ×24 / 76) min$
Here, x = 76 Therefore, required result = $(720/11 - 76) (60 × 24 /76) min$
= $-116/11 × 360/19 min$
= $- 199 169/206 min$ (loss as sign in negative)
Question : 2
The minute hand of a clock overtakes the hour hand at intervals of 58 min of the correct time. How much does a clock gain or lose in a day?
a) 185 $25/319$ min (loss)
b) 185 $25/319$ min (gain)
c) 184 $25/319$ min (loss)
d) 184 $25/319$ min (gain)
Answer »Answer: (b)
Required result =$ (720/11 - x) (60 × 24 / X)$ min Here, x = 58
Therefore, required result = $(720/11 - 62) (60 × 24 /58)$ min
= $82/11 × 720/29 min = 185 25/319 min $gain (gain as sign is positive)
Question : 3
The minute hand of a clock overtakes the hour hand at intervals of 65 min of the correct time. How much does a clock gain or lose in a day?
a) 10 $10/143$ min (gain)
b) 10 $10/143$ min (loss)
c) 6 $10/143$ min (gain)
d) 9 $10/143$ min (loss)
Answer »Answer: (a)
Required result = $(720/11 - x) (60 × 24 /x) $min Here, x = 65
Therefore, required result = $(720/11 - 65) (60 × 24 / 65)$ min
= $5/11 × 288/13$ min = 10 $10/143$ min gain
Question : 4
The minute hand of a clock overtakes the hour hand at intervals of 62 min of the correct time. How much does a clock gain or lose in a day?
a) 81 $80/341$ min (loss)
b) 81 $80/341$ min (gain)
c) 80 $80/341$ min (loss)
d) 80 $80/341$ min (gain)
Answer »Answer: (d)
Required result =$ (720/11 - x) (60 × 24 /x)$ min Here, x = 62
Therefore, required result = $(720/11 - 62) (60 × 24 /62)$ min
= $38/11 × 720/31 $min = 80 $80/341$ min gain (gain as sign is positive)
Question : 5
The minute hand of a clock overtakes the hour hand at intervals of 63 min of the correct time. How much does a clock gain or loses in a day?
a) 54 $8/77$ min (gain)
b) 56 $8/77$ min (gain)
c) 53 $8/99$ min (loss)
d) 54 $8/77$ min (gain)
Answer »Answer: (b)
Method I
As we know that in a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min.
To be together again, the minute hand must gain 60 min over the hour hand.
60 min are gained in $(60/55 × 60) min = 65 5/11 min$
But they are together after 63 min.
Therefore, gain in 63 min =$ (65 5/11 - 63) = 2 5/11 min = 27/11 min$
Gain in 24 h = $(27/11 × 60 × 24/63) min = 4320/77 min = 56 8/77 min$
As result is positive, therefore clock gains 56 $8/77$ min.
Method II
In the given question, x = 63 min
According to the formula,
Required result = $(720/11 - x) (60 × 24 /x) min = (720/11 - 63) (60 × 24 /63 ) min$
= $27/11 × 60 × 8 /21 = 56 8/77 $min (gain as sign in positive)
IMPORTANT verbal reasoning EXERCISES
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