A man cycles at the speed of$8$ km/hr and reaches office at $11$ am and when he cycles at the speed of $12$ km/hr he reaches office at $9$ am. At what speed should he cycle so that he reaches his office at $10$ am?

The average of five numbers is $7$. If three new numbers would be added, then the new average comes out to be $8.5$. What is the average of those three new numbers?

In an election, $10\%$ of the voters on the voters' list did not cast their votes and $60$ voters cast their ballot papers blank. There were only two candidates. The winner was supported by $47\%$ of all the voters in the list, and he got $308$ votes more than his rival. The number of voters on the list was?

Which is the largest among the numbers $\sqrt{5} , 3\sqrt{7} , 4\sqrt{13}$.

A moneylender claims to lend money at the rate of $10\%$ per annum simple interest. However, he takes the interest in advance when he lends a sum for one year. At what interest rate does he lend the money actually?

For $Rs.25500$, a furniture shop sells $3$ computer tables and $5$ chairs or $2$ computer tables and $9$ chairs. If one wants to buy a set of only $1$ computer table and $1$ chair, how much does he need to pay?

A shopkeeper has $11$ books of same cost price. He sells the first book at a certain price, then he sells second book at a price which is $Rs.1$ less than the selling price of first book, and then he sells third book at a price which is $Rs.1$ less than the selling price of second book. Following this pattern, he sold all $11$ books. If he sells sixth book at its cost price, find the overall percentage profit or loss on selling all $11$ books.

After selling a compact disc player for $Rs.13600$, a loss of $15\%$ is incurred. At what price should it be sold to get a profit of $35\%$ on the cost price?