It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
A. 2 : 3
B. 3 : 2
C. 3 : 4
D. 4 : 3
Answer: Option C
Solution (By Examveda Team)
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{be}}\,x\,{\text{km/hr}} \cr & {\text{and}}\,{\text{that}}\,{\text{of}}\,{\text{the}}\,{\text{car}}\,{\text{be}}\,y\,{\text{km/hr}} \cr & {\text{Then}},\,\frac{{120}}{x} + \frac{{480}}{y} = 8 \cr & \Rightarrow \frac{1}{x} + \frac{4}{y} = \frac{1}{{15}}\,.........\left( i \right) \cr & {\text{and}},\,\frac{{200}}{x} + \frac{{400}}{y} = \frac{{25}}{3} \cr & \Rightarrow \frac{1}{x} + \frac{2}{y} = \frac{1}{{24}}\,.........\left( {ii} \right) \cr & {\text{Solving}}\,\left( {\text{i}} \right)\,{\text{and}}\,\left( {{\text{ii}}} \right){\text{,}}\, \cr & {\text{we}}\,{\text{get}},\,x = 60\,{\text{and}}\,y = 80 \cr & \therefore {\text{Ratio}}\,{\text{of}}\,{\text{speeds}} \cr & = 60:80 \cr & = 3:4 \cr} $$This Question Belongs to Arithmetic Ability >> Speed Time And Distance
1/24...because.
after dividing upper part by 25,
8/x + 16/y = 1/3,
now making the numerator small so that during equating we don't have to multiply much.
therefore, again dividing whole equation by 8......which give 1/3x8 = 1/24
1/24 how
For all aspirants here 25/3 was wrote because of mints to hrs changing in the upper math. So 8hr+ 20/60 hr = 25/3 hr.
25/3:
as it takes 20min more , so we'll converting 20 min into hour -> (20/60)=1/3
now we'll add this 1/3 in 8 (as it takes 20min more i.e 8 hour and 20 min)
8+1/3 = 25/3
25/3 how