Question

The ratio of time taken by A and B to travel from Gangtok to Pelling, in Sikkim, is 3:5

respectively. If it takes them 4 hours more to travel from Pelling to Namchi. After travelling

from Pelling to Namchi, the ratio of the time taken by A and B becomes 4:6. Find out the

time taken by A and B to travel from Gangtok to Pelling, in Sikkim.​
PLEASE ANSWER THIS QUESTION ASAP

Answer 1

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Answer 2

Given:

The ratio of time taken by A and B to travel from Gangtok to Pelling = 3:5

Time taken more to travel from Pelling to Namchi = 4hours

The ratio of the time taken by A and B after traveling from Pelling to Namchi = 4:6

To find:

The  time taken by A and B to travel from Gangtok to Pelling.

Solution:

The ratio of time taken by A and B to travel from Gangtok to Pelling = 3:5

Let the time taken by A and B be $3x$hours and $5x$hours respectively, where $x$ is the constant of the proportionality.

Now, according to the given statement, they take 4hours more to travel from Pelling to Namchi

So, the total time taken by A to travel becomes $3x+4$ and the total time taken by B becomes $5x+4$.

Now, the final ratio of their time is 4:6. So,

$\frac{3x+4}{5x+4} =\frac{4}{6}$

Now, we can solve for $x$,

⇒$6(3x+4)=4(5x+4)$

⇒$18x+24=20x+16$

⇒$20x-18x=24-16$

⇒$2x=8$

⇒$x=4$

Therefore,

A takes =  $3x$hours

=(3×4)hours = 12hours

B takes = $5x$hours

=(5×4)hours = 20hours.

Hence, A takes 12 hours and B takes 20 hours to travel from Gangtok to Pelling.