Question

9.
If the two incorrect watches are set at 12:00 noon
at correct time, when will both the watches show
the correct time for the first time given that the first
watch gains 1 min in 1 hour and second water
loses 4 min in 2 hours :
(A) 6 pm, 25 days later
12:00 noon, 30 days later
(C) 12 noon, 15 days later
(D) 6 am 45 days later​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Given That :-

• First watch gains 1 min in 1 Hour.
• 2nd watch loses 4 min in 2 Hours.

So,

→ in 1 day (24hours) first watch gain = 24 * 1 = 24min.

And,

→ in 1 day (24hours) 2nd watch lose = (4 * 24)/2 = 48min.

Therefore,

→ Difference b/w both watches in 1 day = (24 - (-48) = 72 min.

Now, we know That, Both watches will show exact same Time after Difference of 12 Hours.

So,

→ 72 min. Difference = 1 Day.

→ 1 Min. Difference = (1/72)

→ (12*60) Min. Difference = (1/72) * 720 = 10 Days.

Hence, both the watches show the correct time for the first time at :- 12:00 noon + 10 days . = 12:00 noon , 10 days Later. (Ans.) (Option None of These).

[ Note :- 12:00 noon, 30 days later is not correct answer , it is the time when watch shows same time third times . and in Question it is asked for the first time. ]

Answer 2

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$\huge\tt{PROBLEM:}$

• If the two incorrect watches are set at 12:00 noon at correct time.
• when will both the watches show the correct time for the first time given that the first watch gains 1 min in 1 hour and second water loses 4 min in 2 hours ?

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$\huge\tt{SOLUTION:}$

If we start both watch at the same time of 12:00 noon,

➩Time gained by the first watch in one hour = 1 minutes

➩Time gained by the first watch in 24 hours = 24 × 1

➩Time gained by the first watch in 24 hours = 24 minutes

_____________________________________

➩Time gained by the second watch in one hour = 2 minutes

➩Time gained by the second watch in 24 hours = 4 × 24 × ½

➩Time gained by the second watch in 24 hours = 48 minutes

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Hence,

➩Difference of time between the two watches = {24 - (- 48)}

➩Difference of time between the two watches = {24 +48}

➩Difference of time between the two watches = 72 minutes

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We can say that there is a 72 minutes difference in each watch.

Now,

⟹ 72 minutes difference = 1 Day

⟹1 minutes difference = 1/72 Days

⟹ 720 minutes difference = 1/72 × 720 => 10 Days

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