Question

Two clocks are showing the correct time at $4.00\,pm$. One clock loses $3.5$ minutes in an hour, while the other gains $2.5$ minutes in one hour. At $10.00\,pm$ on the same day, by how much time will the two clocks differ?
A. $12$ minutes
B. $36$ minutes
C. $24$ minutes
D. $30$ minutes

Answer 1

Hint: Given in the question there are two clocks with some time and in one one clock the time for one hour loses some minutes while in the other clock the time for one hour gains some minutes. For this here we are going to calculate how many minutes will be differ for two clocks.

Complete step by step answer:
Given in the question is, at time $4.00\,pm$ and at time $10.00\,pm$ from this the difference between both the timings is $6\,hours$, so by this here we are differentiating the two clocks with their respective loses and gains,

First of all lets differ two clocks by A and B. Here we are going to find the clock A, that means the clock A, loses its time that means we are taking negative sign,
$A = - 6 \times 3.5$,
Here $3.5$ is the time loses by A and $6$ is the difference between the given timings,
$A = - 21\,minutes$
For clock B also we are using same method,
\[B = 6 \times 2.5\]

In the above equation $2.5$ is the time gained by clock B,
Therefore, $B = 15\,minutes$
Now we are going to differ the two clocks A and B,
Therefore, $ = B - A$
The differ between two clocks is
$B - A \\
\Rightarrow 15 - \left( { - 21} \right) \\
\Rightarrow 15 + 21 \\
\therefore 36\,minutes $
The difference between the two clocks is $36\,minutes$. Hence the correct option is option (B).

Note: From the given data we have proved the difference between the two clocks, for this calculation in clock A we have assumed it in negative sign because in clock A it was losing its time for this reason we have considered it in negative sign. Thus we have proved the correct solution, the correct option is B.