Question

A watch which gains uniformly is $2$ minutes slow at noon on Monday and is $4$ min $48$ sec fast at $2$p.m. on the following Monday when was it correct?
A. $2$p.m. on Tuesday
B. $2$p.m. on Wednesday
C. $3$ p.m. on Thursday
D. $1$ p.m. on Friday

Answer 1

Hint: First, we should analyze the given data so that we are able to solve the problem. We need to calculate the total time from noon on Monday to $2$p.m. on the following Monday. Next, we need to find the watch gains in two minutes. Then, we shall find the required corrected time after $12$ p.m. on Monday

Complete step-by-step answer:
First, we shall calculate the total time from noon on Monday to $2$p.m. on the following Monday.
Number of days from $12$ p.m. on Monday to $2$p.m. on the following Monday $ = 7$
That is seven days are there from $12$ p.m. on Monday to $2$p.m. on the following Monday.
Now, we shall convert days into hours.
We know that $1day = 24hours$
Hence, $7days = 7 \times 24hours$
$ \Rightarrow 7days = 168hours$
Also, it is given that time is $2$p.m. on the following Monday and so there will be an extra two hours.
Hence, the total time from noon on Monday to $2$p.m. on the following Monday$ = 168 + 2$
     $ = 170hours$
Thus, the time from $12$ p.m. on Monday to $2$p.m. on the following Monday$ = 170hours$
Also, we are given that the watch gains $2minutes + 4minutes48seconds$
$ \Rightarrow 2minutes + 4\dfrac{{48}}{{60}}minutes$
$ \Rightarrow 2minutes + 4\dfrac{4}{5}minutes$ (Here we applied $1seconds = \dfrac{1}{{60}}minutes$ )
$ \Rightarrow 2minutes + \dfrac{{24}}{5}minutes$

$ \Rightarrow \dfrac{{10 + 24}}{5} minutes$
$ \Rightarrow \dfrac{{34}}{5}minutes$
Hence the watch gains $\dfrac{{34}}{5}minutes$in $170hours$
We shall find how many hours a watch take to gain in one minute.
That is, the watch gains $1\min ute$ in $170 \times \dfrac{5}{{34}}hours$
Also, we need to calculate how many hours a watch takes to gain in two minutes.
Thus, the watch gains $2$ minutes in $170 \times \dfrac{5}{{34}} \times 2hours$

Hence, the watch gains $2$ minutes in $50hours$

We know that $50hours$is equal to $2days2hours$.
Hence, the watch is corrected at $2days2hours$ after $12$ p.m. on Monday
Therefore, after $12$ p.m. on Monday, the watch is corrected at $2$p.m. on Wednesday
Thus, the required answer is $2$p.m. on Wednesday and option B is correct.

So, the correct answer is “Option B”.

Note: While converting into the same units, we may get confused whether we need to multiply or divide the required number. While converting larger units into small units, we need to multiply and while converting smaller units into larger units, we need to divide.
Here, to convert days into hours, we need to multiply $24$ , and to convert seconds into minutes, we need to divide by $60$