Find the sum of those integers from $1$ to $500$ which are multiples of $2$ as well as of $5$.

In a school,students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees,that each section of each class will plant,will be the same as the class,in which they are studying,e.g.,a section of Class $I$ will plant $1$ tree,a section of Class $II$ will plant $2$ trees and so on till Class $XII$. There are three sections of each class. How many trees will be planted by the students?

Find the sum of the first $30$ terms of the $A.P.$ $15, 20, 25, \ldots$

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 5 - 6n$. Find the sum of the first $n$ terms of the $A.P.$

For a given $A.P.$,$S_{10} = 50$ and $a = 0.5$. Then,$d = \ldots \ldots \ldots . .$

$A$ contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ $200$ for the first day,₹ $250$ for the second day,₹ $300$ for the third day,etc. The penalty for each succeeding day is ₹ $50$ more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by $30$ days?