Question

A clock is set to show the correct time at $11AM$ on Sunday. If the clock gains $12$ minutes in $12$ hours, then what will be the time when watch indicates $1PM$ on the Friday?

• A. $10AM$
• B. $11AM$
• C. $12noon$
• D. None of these

Answer 1

Answer: (B)

$11AM$

$\text{Approach 1:}$

It is given that clock gains $12min$ in $12hours$.

$⟹$ Clock gains $1min$ in every $1hour$.

Total number of hours from Sunday $11AM$ to Friday $1PM$ are $122$

Now,

New clock shows $61mins$ in $60min$ of true clock.

$⟹$ New clock shows $\frac{61}{60}hours$ in $1hour$ of true clock.

So, when new clock shows $122hours$, then the true clock shows $\frac{60}{61}\times 122hours=120hours$

So the time true clock shows after $120hours$ from Sunday $11AM$ is $11AM$ on Friday.

Hence, option B.

$\text{Approach 2:}$

It is given that clock gains $12min$ in $12hours$.

$⟹$ Clock gains $1min$ in every $1hour$.

Let assume today's clock is set and is Sunday so $6^{th}$ day it will Friday.
Now, from $11AM$ of Sunday to $12AM$ of Monday, it gains $13min$ in these $13hours$.

Now, total hours from Monday $12AM$ to Friday $12AM$ are $96$

Therefore, clock gains $96mins$ in these $96hours$
And from Friday $12AM$ to Friday $11AM$, number of hours are $11$

So, clock gained $11mins$ in these $11hours$ also.

So Total number of actual hours $=13+96+11=120$

And clocked also gained $120mins$.

So the clock shows $2hours$ more than the actual time.

But right now, the clock is showing $1PM$

$\therefore$ the actual time is $11AM$ of Friday.

$B$ is right answer.