Question 88

A person rows a distance of 12 kms in down stream and returns to the starting point. The difference between the times taken to travel in down stream and that of upstream is 6 hours. If he doubles his speed throughout the above trip, then the difference between the times taken to cover in down stream and upstream is 1 hour. Then the speed of the current in km per hour is

Solution

Let say, speed of the boat is b km/h and speed of the current is c km/h.

So, in downstream speed is (b+c) km/h and in upstream speed is (b-c) km/h.

Time taken in downstream=(12/(b+c)) h.

and time taken in upstream=(12/(b-c)) h.

So, according to question:

$$(12/(b-c))-(12/(b+c))=6.$$

or,$$(b+c-b+c)/(b^2-c^2)=(1/2).$$

$$b^2-c^2=4c.$$

$$b^2=c^2+4c.$$..............(1)

if speed of speed is doubled ,then speed in downstream =(2b+c) km/h .

and speed in upstream=(2b-c) km/h.

So, time taken in downstream 12/(2b+c) h.

And time taken in upstream 12/(2b-c) h.

So,

$$12/(2b-c)-12/(2b+c)=1$$

or,$$(2b+c-2b+c)/(4b^2-c^2)=(1/12)$$

or,$$24c=4b^2-c^2$$

or,$$b^2=(c^2+24c)/4.$$........(2)

So,from (1) & (2) :

$$(c^2+24c)/4=c^2+4c.$$

or,$$c^2+24c=4c^2+16c$$

or,$$3c^2=8c$$

or,$$c=8/3$$

So,speed of current is 8/3 km/h.

A is correct choice.