Question

Moving at ${\text{50kmph}}$ a person reaches his office $10$ minute late next day he increases his speed and moves at ${\text{60kmph}}$ and reaches his office $5$ minute girly what is the distance from his home to his office?
A) ${\text{75km}}$
B) ${\text{70km}}$
C) ${\text{80km}}$
D) ${\text{77km}}$

Answer 1

Hint: Let the distance of office from his home be $\text{xkm}$, let at speed ${\text{v}}$ he reaches office in time ${\text{t}}$ now at speed ${\text{50kmph}}$ he reaches office in time $\left( {{\text{t + 10}}} \right)$ minutes and at speed ${\text{60kmph}}$ he takes $\left( {{\text{t - 5}}} \right)$ minutes to reach the office ,So we know that speed $ = \dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$ and distance is the same for both speeds.Using these definitions and formulas try to get the answer.

Complete step-by-step answer:
Let at moving speed ${\text{v}}$ he reaches office in ${\text{t}}$ time and let us assume the distance of office from his home be ${\text{x km}}$ and according to the question when he moves at ${\text{50kmph}}$ he reaches his office ${\text{10 min}}{\text{.}}$ later that mean if he take ${\text{t min}}{\text{.}}$ to reach the office then at ${\text{50kmph}}$ he took $\left( {{\text{t + 10}}} \right)$ minutes.
And we know that speed $ = \dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$
We know ${\text{1km = 1000m & 1 Hours = 60 minutes}}$
So $1{\text{ km per hour = }}\dfrac{{{\text{1 km}}}}{{{\text{1 hour}}}}$
When we convert hours into minutes $1{\text{ km per hour = }}\dfrac{{{\text{1 }}}}{{60}}{\text{km per minute}}$
So ${\text{50 kmph can be written as }}\dfrac{{50}}{{60}}{\text{km per minute}}$
As we are taking time in minutes and distance in kilometer so we need to convert the hours in minutes so as we assume the distance $ = x$
So ${\text{ }}\dfrac{{50}}{{60}}{\text{km per minute = }}\dfrac{{\text{x}}}{{{\text{t + 10}}}}{\text{km per minute}}$
We get $\dfrac{{{\text{50}}}}{{{\text{60}}}}{\text{ = }}\dfrac{{\text{x}}}{{{\text{t + 10}}}}$
Now if he walks with speed then he reaches the office early so at speed ${\text{60kmph}}$ he took $\left( {{\text{t - 5}}} \right)$ minutes as we need to convert ${\text{kmph}}$ into kilometer per minute and we know $1{\text{ km per hour = }}\dfrac{{{\text{1 }}}}{{60}}{\text{km per minute}}$
So $6{\text{0kmph = }}\dfrac{{{\text{60}}}}{{{\text{60}}}}{\text{ = 1 km per minute}}$
and distance we assume $x$
Then, ${\text{speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$
We got ${\text{1 = }}\dfrac{{\text{x}}}{{{\text{t - 5}}}}$
${\text{x = t - 5}}$
putting value of $x$ in equation
$\dfrac{{50}}{{60}} = \dfrac{{t - 5}}{{t + 10}}$
Upon cross multiplication
$\begin{gathered}
  {\text{5(t + 10) = 6(t - 5)}} \\
  {\text{5t + 50 = 6t - 30}} \\
  {\text{80 = t}} \\
\end{gathered} $
We got time$ = {\text{80minute}}$
Therefore we know
${\text{x = t - 5}}$, where x is in km and t is in minute
$ {\text{x = 80 - 5 = 75 km}}$
Hence,The distance from his home to his office is $75km$.

Note:The given formula speed $ = \dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$ is given valid only when speed remains constant or when acceleration is zero if acceleration is given a then speed $ = \dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$ is not valid as acceleration is the rate of change of speed so speed will not be constant.