SSC CGL 20191)Abhi rows upstream a distance of 28 km in 4 hours and rows downstream a distance of 50 km in 2 hours. To row a distance of 44.8 km in still water, he will take :
2.8 hours
Let the speed of boat be x and speed of stream be y.
Abhi rows upstream a distance of 28 km in 4 h.
So, speed in upstream = 28/4 = 7 km/hr;
x - y = 7 ---(1);
Abhi rows downstream a distance of 50 km in 2 h.
So, speed in downstream = 50/2 = 25 km/hr;
x + y = 25 ---(2);
On eq (1) + (2),
2x = 32;
x = 16;
Time taken to row a distance of 44.8 km in still water = 44.8/16 = 2.8 hr
SSC CGL 20192)A train travelling at the speed of x km/h crossed a 200 m long platform in 30 seconds and overtook a man walking in the same direction at the speed of 6 km/h in 20 seconds. What is the value of x ?
60
Length the length off the traiin be l m.
A train travelling at the speed of x km/h crossed a 200 m long platform in 30 seconds;
So, length = speed \times time;
(l + 200) = 30x;
l = 30x - 200 ---(1);
Speed of man = 6 km/hr = \(6 \times \frac{5}{18} \)= 5/3 m/sec;
Relative speed = x - 5/3;
\(\frac{l}{20} = \frac{3x - 5}{3};\)
put the value of l,
\(\frac{30x - 200}{20} = \frac{3x - 5}{3}; 90x - 600 = 60x - 100;\)
30x = 500;
x = 50/3 m/sec = \(\frac{50}{3} \times \frac{18}{5} \)= 60 km/hr
SSC CGL 20193)A and B started their journeys from X to Y and Y to X, respectively. After crossing each other, A and B completed the remaining parts of their journeys in \( 6\frac{1}{8}\) hours and 8 hours respectively. If the speed of B is 28 km/h, then the speed (in km/h) of A is:
32
By the formula,
Ratio of the speed =\( \sqrt{\ inverse\ \ ratio\ \ of\ \ the time}\);
\(\frac{S_a}{S_b} = \sqrt{\frac{t_b}{t_a}};\)
\(S_b = 28 km/hr;\)
\(t_a \)= \(6\frac{1}{8} = \frac{49}{8};\)
\(t_b \)= 8;
\(\Rightarrow \frac{S_a}{28} = \sqrt{\frac{8}{\frac{49}{8}}};\)
\(\Rightarrow \frac{S_a}{28} = \sqrt{\frac{64}{49}};\)
\(\Rightarrow \frac{S_a}{28} = \frac{8}{7};\)
\(S_a = 32 km/hr\)
SSC CGL 20194)A man can row a distance of 900 metres against the stream in 12 minutes and returns to the starting point in 9 minutes. What is the speed (in km/h) of the man in still water?
\(5\frac{1}{4}\)