The numbers $1, 2, \ldots, 9$ are arranged in a $3 \times 3$ square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value. If the top left and the top right entries of the grid are $6$ and $2$, respectively, then the bottom middle entry is:

In a $10\text{ km}$ race, $A$, $B$, and $C$, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If $A$ beats $B$ by $1\text{ km}$ and $B$ beats $C$ by $1\text{ km}$, then by how many metres does $A$ beat $C$?

Bottle 1 contains a mixture of milk and water in $7:2$ ratio and Bottle 2 contains a mixture of milk and water in $9:4$ ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in $3:1$ ratio?

Arun drove from home to his hostel at $60$ miles per hour. While returning home he drove half way along the same route at a speed of $25$ miles per hour and then took a bypass road which increased his driving distance by $5$ miles, but allowed him to drive at $50$ miles per hour along this bypass road. If his return journey took $30$ minutes more than his onward journey, then the total distance travelled by him is:

Out of the shirts produced in a factory, $15\%$ are defective, while $20\%$ of the rest are sold in the domestic market. If the remaining $8840$ shirts are left for export, then the number of shirts produced in the factory is

The average height of $22$ toddlers increases by $2$ inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original $22$, then the average height, in inches, of the remaining $20$ toddlers is

The manufacturer of a table sells it to a wholesale dealer at a profit of $10\%$. The wholesale dealer sells the table to a retailer at a profit of $30\%$. Finally, the retailer sells it to a customer at a profit of $50\%$. If the customer pays $\text{Rs } 4290$ for the table, then its manufacturing cost (in Rs) is

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in $8$ hours. If the outlet pipe is open then the inlet pipe fills the empty tank in $10$ hours. If only the outlet pipe is open then in how many hours does the full tank become half-full?

Mayank buys some candies for $\text{Rs } 15$ a dozen and an equal number of different candies for $\text{Rs } 12$ a dozen. He sells all for $\text{Rs } 16.50$ a dozen and makes a profit of $\text{Rs } 150$. How many dozens of candies did he buy altogether?

In a village, the production of food grains increased by $40\%$ and the per capita production of food grains increased by $27\%$ during a certain period. The percentage by which the population of the village increased during the same period is nearest to