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29 Jan 2021, 06:15
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B
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Difficulty:
85%
(hard)
Question Stats:
54% (02:33) correct
46%
(02:54)
wrong
based on 140
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A man sets out on cycle from Bina to Itarsi and at the same time another man starts from Itarsi to Bina on cycle. After passing each other they complete their journeys in 16 and 25 hours respectively. At what rate does the second man cycle if the first cycles at 15 km/h?
(A) 15 km/h
(B) 12 km/h
(C) 10 km/h
(D) 8 km/h
(E) 6 km/h
(A) 15 km/h
(B) 12 km/h
(C) 10 km/h
(D) 8 km/h
(E) 6 km/h
29 Jan 2021, 09:31
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Concept:
\(A\)--------\({t_1}\)----------\(X\)---------\({t_2}\)---------\(B\)
A and B start walking towards each other. After meeting A covers his distance in \(t_1\) time and B covers his distance in \(t_2\) time. The ratio of their speed is;
\(\frac{S_A}{S_B}=\sqrt{\frac{t_2}{t_1}}\)
Based on this concept,
\(\frac{S_A}{S_B}=\sqrt{\frac{16}{25}} = \frac{4}{5}\)
\(S_B=5--->15\)
\(S_B--->3\)
\(S_A=4*3=12\) km/hr
Ans B
\(A\)--------\({t_1}\)----------\(X\)---------\({t_2}\)---------\(B\)
A and B start walking towards each other. After meeting A covers his distance in \(t_1\) time and B covers his distance in \(t_2\) time. The ratio of their speed is;
\(\frac{S_A}{S_B}=\sqrt{\frac{t_2}{t_1}}\)
Based on this concept,
\(\frac{S_A}{S_B}=\sqrt{\frac{16}{25}} = \frac{4}{5}\)
\(S_B=5--->15\)
\(S_B--->3\)
\(S_A=4*3=12\) km/hr
Ans B
General Discussion
26 Mar 2024, 11:20
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meanup
If anyone is curious how this formula is derived.
Let's assume that speed of A is a, Speed of B is b. They meet each other after time 't' has been elapsed after starting.
Total distance is = a*t + b*t
individually A takes t+16 hours and B takes t+25 hours to complete the total disrance.
So the total distance (in terms of speed of A) is = a*(t+16) and that by B is = b*(t+25)
Now we have two equations
a*t + b*t = a*(t+16) = b*(t+25)
solving this we get 16*a^2= 25*b^2. i.e. \(\frac{a}{b}=\sqrt{\frac{{t_2}}{{t_1}}}\)
from here we can get the answer b=12
Ans B
