Exercise

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 $50 kmph$.

In a garage, there are some two-wheelers and four wheelers. The total number of wheels of these are $30$more than twice the total number of these vehicles. Find the number of four wheelers.

 The value of the ones digit of a $3$-digit number is three times the hundreds digit and twice the tens digit. Find the number.

If one-third of a number $x$ is subtracted from two-thirds of the number $x$, then the result is $6$. Then, $x=$ _____.

The sum of the ages of a man and his daughter is $56$ years. If the daughter's age is $\frac{1}{3}$ of his father' age, then find the age (in years) of the daughter.

Solve the following equations.

$2y+\frac{5}{2}=\frac{37}{2}$

The minute hand of a clock is $14 \mathrm{cm}$ long. How far does the tip of the minute hand move in $60 \min$? [Take $\mathrm{\pi }=\frac{22}{7}$]

In the given figure, $O$ is the centre of the circle, $\angle AOB=60°$ and the radius of the circle is $6 \mathrm{cm}$. Find the area of the triangle $OAB$.