Question

A clock is set right at 12 noon on monday. It loses 1/2% on the correct time in the first week but gains 1/4% on the true time during the second week. The time shown on monday after two weeks will be

Answer 1

Answer :

The number of hours in a week = 24*7 = 168.

Week 1: The clock loses (1/2)% of the actual time

To LOSE time is to OVERCOUNT the number of hours.

Let's say that we must leave a party at 2pm.

if the clock overcounts the number of hours and reads 2pm when the time is really 1pm, we will leave 1 hour EARLIER than is necessary, with the result that we LOSE one hour of party time.

Here, the number of hours OVERCOUNTED = (1/2)/100 * 168 = 84/100 = .84 hours.

Thus, at the end of week 1, the clock is AHEAD .84 hours.

Week 2: The clock gains (1/4)% of the actual time

To GAIN time is to UNDERCOUNT the number of hours.

Let's say we that we must leave a party at 2pm.

If the clock undercounts the number of hours and reads 1pm when the time is really 2pm, we will leave the party 1 hour LATER than is necessary, with the result that we GAIN one hour of party time.

Here, the number of hours UNDERCOUNTED = (1/4)/100 * 168 = 42/100 = .42 hours.

In other words, the clock MOVES BACK .42 hours.

Net change for the two weeks = .84 - .42 = .42 hours.

Since 1 hour = 60 minutes, we get:

(1 hour)/(60 minutes) = (.42 hours)/(x minutes)

x = .42(60) = 25.2 minutes = 25 minutes, 12 seconds.

Since the clock is AHEAD by 25 minutes, 12 seconds, the time shown = 12:25:12.

I HOPE THIS ANSWER HELPS YOU...

Answer 2

Answer:

he time shown on Monday after time period are going to be $12:25:12$.

Step-by-step explanation:

It is on condition that the clock is about at $12$ noon on Monday and it's also only if in first-week clock loses $\frac{1}{2}\%$ and in second week clock gains $\frac{1}{4}\%$ on true time.

The number of hours during a week is $24\times 7=168$.

To LOSE time is to OVERCOUNT the amount of hours and to realize time is to UNDERCOUNT the quantity of hours.

Firstly, we'll find the quantity of hours overcounted in first week is

$\frac{\frac{1}{2}} {100}\times 168=0.84$ hours

Thus, at the tip of first week , the clock is AHEAD $0.84hrs$.

Now, we are going to find the quantity of hours undercounted in second week is

$\frac{\frac{1}{4}}{100}\times 168=0.42$

Thus, the clock MOVES BACK $0.42hrs$

Further, we'll find the online change of time period, we get

$0.84-0.42=0.42hrs$

Furthermore, we'll convert this times into minute by multiplying with $60$

we get

$0.42\times 60=25.2min$ or $25\text{minutes },12\text{seconds}$.

Thus, the time shown is $12:25:12.$

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