Three partners $A$, $B$ and $C$ entered into a business. $A$ invested one-third of the capital for one-third duration. $B$ invested one-fourth of the capital for one-fourth duration. $C$ invested the remaining capital for the whole duration. Out of a profit of ₹ $17,000$, how much profit will $C$ get?

A shopkeeper employs a delivery boy and gives him a motorcycle for home delivery. For every delivery, the boy is given ₹ $5$. At the end of the day, he also gets ₹ $2$ for every kilometre of the distance covered in the day. The boy wants to earn more than ₹ $500$ a day, but does not want to travel more than $100$ km. Which of the following numbers of deliveries would definitely meet his target?

A toy $T$ jumps forward or backward. In each forward jump, it moves $5'$ forward whereas in each backward jump, it moves $2'$ backward. If in $31$ jumps, $T$ moves exactly $15'$ forward, then what is the difference of the number of forward and backward jumps?

In a recruitment process, the selection of candidates is based on their performance in three components. The weightages of the components 1, 2 and 3 are $0.2$, $0.3$ and $0.5$, respectively. Use the data given below and find the cutoff score if exactly three candidates are to be selected :

There are two chemicals which do not react with each other. A container contains $10$ litres of the chemical $A$. One litre of this chemical is removed from it and one litre of the chemical $B$ is poured. Then one litre of the mixture is removed from the container and one litre of $B$ is poured. If this process of replacing one litre of the mixture by one litre of $B$ is performed once more, then what is the volume of $B$ that is present in the container approximately (in percentage)?

If $x$ and $y$ are integers, then is $x$ even? Statement I : $x^2 y^2$ is even. Statement II : $1 + x^2 + y^2$ is odd.