It takes 8, hours for a 600, km journey,if 12 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the speed of the train be $v_t\, km/hr$ and the speed of the car be $v_c\, km/hr$.Case $1$: $\frac{120}{v_t} + \frac{480}{v_c} = 8$  --- $(1)$

Vedclass · Accepted Answer

$3:4$

Vedclass · Answer

(C) Let the speed of the train be $v_t\, km/hr$ and the speed of the car be $v_c\, km/hr$.Case $1$: $\frac{120}{v_t} + \frac{480}{v_c} = 8$  --- $(1)$Case $2$: $\frac{200}{v_t} + \frac{400}{v_c} = 8 + \frac{20}{60} = 8 + \frac{1}{3} = \frac{25}{3}$  --- $(2)$Divide $(1)$ by $40$: $\frac{3}{v_t} + \frac{12}{v_c} = \frac{1}{5}$  --- $(3)$Divide $(2)$ by $200$: $\frac{1}{v_t} + \frac{2}{v_c} = \frac{25}{3 	imes 200} = \frac{1}{24}$  --- $(4)$Multiply $(4)$ by $3$: $\frac{3}{v_t} + \frac{6}{v_c} = \frac{3}{24} = \frac{1}{8}$  --- $(5)$Subtract $(5)$ from $(3)$: $(\frac{12}{v_c} - \frac{6}{v_c}) = \frac{1}{5} - \frac{1}{8} \Rightarrow \frac{6}{v_c} = \frac{8-5}{40} = \frac{3}{40} \Rightarrow v_c = \frac{6 	imes 40}{3} = 80\, km/hr$.Substitute $v_c = 80$ in $(4)$: $\frac{1}{v_t} + \frac{2}{80} = \frac{1}{24} \Rightarrow \frac{1}{v_t} = \frac{1}{24} - \frac{1}{40} = \frac{5-3}{120} = \frac{2}{120} = \frac{1}{60} \Rightarrow v_t = 60\, km/hr$.Ratio of speed of train to car $= v_t : v_c = 60 : 80 = 3 : 4$.

It takes $8\, hours$ 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 car is

Similar Questions

If a boy travels from his house to school at the rate of $4 \, km/h$,he reaches the school $10 \, minutes$ earlier than the scheduled time. However,if he walks at the rate of $3 \, km/h$,he reaches $10 \, minutes$ late. Find the distance of the school from his house (in $km$).

The speed of a car increases by $2\, km/h$ after every hour. If the distance travelled in the first hour was $35\, km$,what is the total distance travelled in $12$ hours? (in $km$)

$A$ train running at the speed of $84 \, km/h$ passes a man walking in the opposite direction at the speed of $6 \, km/h$ in $4 \, s$. What is the length of the train (in $meters$)?

It takes $8 \, \text{hours}$ for a $600 \, \text{km}$ journey if $120 \, \text{km}$ is covered by train and the rest by car. It takes $20 \, \text{minutes}$ more if $200 \, \text{km}$ is covered by train and the rest by car. The ratio of the speed of the train to that of the car is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module