(solved)Question 2 SSC-CGL 2020 March 5 Shift 1

X and Y are two points in a river. Points P and Q divide the straight line XY into three equal parts. River is flowing along XY and the time taken by the boat to row from X to Q and from Y to Q are in the ratio 4 : 5. The ratio of the speed of the boat downstream to the speed of the current is?
(Rev. 10-May-2024)

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Question 2SSC-CGL 2020 Mar 5 Shift 1

X and Y are two points in a river. Points P and Q divide the straight line XY into three equal parts. River is flowing along XY and the time taken by the boat to row from X to Q and from Y to Q are in the ratio 4 : 5. The ratio of the speed of the boat downstream to the speed of the current is?

Solution in detail

It is better to first draw a rough diagram (see the attached video).

And since we have to deal with ratios, take XY = 3. So XQ = 2, and YQ = 1.

First take the journey XQ. Time taken is 4 units. Hence, by time distance formula downstream speed is

$\displaystyle D = \frac{\text{distance}}{\text{time}} = \frac{2}{4} = \frac12$

Now take the journey YQ. Time taken is 5 units, distance is 1. Hence, by time distance formula upstream speed is:

$\displaystyle U = \frac{1}{5}$

Speed of current by shortcut formula is (D - U)/2

$\displaystyle \therefore C = \frac{D - U}{2} = \frac{\frac12 - \frac15}{2} = \frac{3}{20}$

Hence the ratio of downstream speed to that of the speed of the current is

$\displaystyle \frac{D}{C} = \frac{(\frac12)}{(\frac{3}{20})} = 10 : 3 \:\underline{Ans}$