Question

$\large{\boxed{\sf{\pmb{\pink{Question:-}}}}}$
By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
A. 15 kmph
B. 20 kmph
C. 25 kmph
D. 30 kmph
$\large{\bold{\underline{no \: spam}}}$
​

Answer 1

let distance travelled = x km

$\sf \: Time \: taken = x /40 hr.$

Now, he has travelled 2x/3 km

(2/3 of the distance) in x/120 hr.

$\rm \: (1/3 \: of \: the \: total \: time)$

distance to be travelled = x/3 km.

Available time = x/60 hr.

required speed =

$\tt \red { ( x / 3) / ( x /60) = 20 kmph.}$

Then we will get the answer 20 kmph.

______________________________________

Answer 2

Given:

By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time.

To find:

What speed should he maintain for the remaining distance to reach his destination on time?

Concept:

Speed is defined as the rate of change of position of an object in any direction. It's calculated as the distance travelled divided by the amount of time it took to travel that distance.

$\;\red{\boxed{\gray{\;\textsf{\textbf{Speed}}=\dfrac{\textsf{\textbf{Distance}}}{\textsf{\textbf{Time taken}}}\;}}}$

Calculations:

Let us assume that, the time taken to reach the destination be 3t hours.

We know, the distance is the product of speed and time covered by the vehicle.

So, total distance = 40 × 3t = 120t km.

As it is given that, he covered two-third the total distance in one-third of the total time. Therefore,

$\begin{array}{l}\rm{= \dfrac{2}{3} \times 120t} \\ \\ \rm{= 2 \times 40t} \\ \\ \rm{= 80t}\end{array}$

And,

$\begin{array}{l}\rm{= \dfrac{1}{3} \times 3t} \\ \\ \rm{= 1 \times t} \\ \\ \rm{= t}\end{array}$

So, now, he covered 80t km distance in t hours time.

So, the remaining distance 120t - 80t = 40t km, he has to cover in 3t - t = 2t hours time.

• Distance = 40t km

• Time taken = 2t hours

Now, by using the speed formula and substituting the known value in it we get:

$\begin{array}{l}\rm{\implies Speed = \dfrac{Distance}{Time\;taken}} \\ \\ \implies \rm{Speed = \dfrac{40t}{2t}} \\ \\ \implies \rm{Speed = \dfrac{40}{2}} \\ \\ \implies \rm{Speed = 20 \; kmph}\end{array}$

Hence, the required speed to reach destination on time is 20 kmph. So, option (B) is correct.