A boat sails downstream from a point P to point Q which is 24 km away from P and then returns to P I...........

Quantitative Aptitude (MTS) Boats and Streams

A boat sails downstream from a point P to point Q, which is 24 km away from P, and then returns to P. If the actual speed of the boat (in still water) is 6 km/h, the entire trip from P to Q takes 3 hours less than that from Q to P. What should be the actual speed (in km/h) of the boat to sail from P to Q in 2 hours?

This questions was previously asked in

SSC MTS 8th October 2021 Shift-1

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Explanation:

Correct option is - 10 Km/hr

Solution

Let speed of stream be x km/hr
Distance between P and Q = 24 km
Time taken to travel upstream Q to P = 24/(6-x)
Time taken to travel downstream P to Q = 24/(6 + x)
Now,
⇒24/(6-x)-24/(6 + x) = 3
⇒24(6+x-6+ x)/(62 - x2) = 3
⇒ 8(x + x)/(36-x2) = 1
⇒ 16x=36-x2
⇒x2+16x-36 = 0
=> x2-2x+18x-36 = 0
x(x-2)+18(x-2) = 0 (x-2) (x + 18) = 0
⇒x=2 or -18
Now,
The actual speed of boat to sail from P to Q in 2 hours = 24/(B+W) = 2
24/(B+ 2) = 2
⇒ 12 = B + 2
=
⇒ B = (12-2)
B = 10 km/h