Subject Experts Solutions for Chapter: Ratio and Its Applications, Exercise 2: PRACTICE QUESTIONS (COMPETITION WING)

A train overtakes a person walking at $1 m/s$ in $5 s$. If the speed of the train is $65 m/s$, then what is the length of the train?

Two trains travelling in opposite direction at $60 kmph$ and $50 kmph$ crossed each other in $9 s.$ If the train which is travelling at $60 kmph$ crossed a pole in $6 s,$ then find the length of the train which is travelling at $50 kmph$.

Two trains are travelling in opposite direction at $72 km/h$ and $90 km/h$. They cross each other in $16 s$. If the length of the slower train is $320 m$, then find the length of the faster train (in $m$)

Two pipes $P_1$ and $P_2$ can fill a tank in $6 h$ and $3 h$, respectively. Both the pipes are opened simultaneously and pipe $P_1$ is closed after $1 h$. Find the time taken by $P_2$ to fill the remaining part of the tank (in hours).

In a class, there are $30$ boys and $20$girls. The average weight of $30$ boys is $60 kg$ and the average weight of $20$ girls is $35 kg$. Find the average weight of the class.

Radha takes $4 h$ to travel from her village to her friend's city by bus. If she goes by car, whose speed is $\frac{2}{3}$ times that if the bus, then how much time will she take to cover the same distance?

A pipe can fill an empty tank in $12 h$. After it is kept open for $3 h$, another pipe which can fill the tank in $8 h$ is opened. In how many more hours will the tank be filled ?

Anil invested a sum of money at a certain rate of simple interest for a period of five years. Had he invested the same sum for a period of eight years for the same rate, the total interest earned by him would have been sixty percent more than the earlier interest amount. Find the rate of interest p.a.