There are two trains, Train P and Train Q. Both the trains have four different types of coaches, viz Sleeper, AC Tier $\mathrm{III},$Tier II and Tier $\mathrm{I}$. In train P, there are a total of $3000$ passengers. Train Q has $40\%$more passengers than Train P.$30\%$ of the passengers in Train P are in sleeper coaches. One – third of the total number of passengers in Train P are in AC Tier$\mathrm{I}. 18 \%$ of the passengers in Train P are in AC Tier $\mathrm{II}$ and the remaining are in AC Tier $\mathrm{III}. 40\%$ of the total number of passengers of Train Q are in Sleeper coaches. In Train Q, the ratio of the passengers of AC Tier $\mathrm{III},$ Tier $\mathrm{II}$ and Tier$\mathrm{I}$ is $4: 3: 2$.

 The costs per ticket of train P for AC tier$\mathrm{III}$and Tier $\mathrm{I}$ are $₹1800 \text{and} ₹3000$ respectively. Then find the total amount generated by both the coaches in Train P:

Direction: In a University there are $1200$ students studying four different subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

What is the difference between the number of boys studying Mathematics and the number of girls studying Physics?

Consider the following for the question that follows:

$500$ candidates appeared in an examination comprising tests in English, Hindi and Mathematics. $30$ candidates failed in English only; $75$ failed in Hindi only; $50$ failed in Mathematics only; $15$ failed in both English and Hindi; $17$ failed in both Hindi and Mathematics; $17$ failed in both Mathematics and English; $5$ failed in all three tests.

In a University there are $1200$ students studying four different subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

What is the ratio of the total number of boys to the total number of girls?

Direction: In a University there are $1200$ students studying four different subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

In which subjects is the difference between the number of boys and girls equal?

$ABC$ is a triangle with $AB=1.6 \mathrm{cm}, BC=6.3 \mathrm{cm} \text{and} CA=6.5 \mathrm{cm}$. Let $P \text{and} Q$ be the mid-points of $AB and BC$ Respectively.

What is $4\left(C{P}^2-A{Q}^2\right)$ equal to?

Direction: In a University there are $1200$ students studying four difference subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

What is the total number of boys studying Statistics and Physics?

Consider the following for the question that follows:

$500$ candidates appeared in an examination comprising tests in English, Hindi and Mathematics. $30$ candidates failed in English only; $75$ failed in Hindi only; $50$ failed in Mathematics only; $15$ failed in both English and Hindi; $17$ failed in both Hindi and Mathematics; $17$ failed in both Mathematics and English; $5$ failed in all three tests.

Direction: Consider the following for the next 04 (four) items that follow:

In an examination of Class XII, $55\%$ of students passed in Biology, $62\%$ passed in Physics, $60\%$ passed in Chemistry, $25\%$ passed in Physics and Biology, $30\%$ passed in Physics and Chemistry, $28\%$ passed in Biology and Chemistry. Only $2\%$ failed in all the subjects.

What percentage of students passed in exactly one subject?

Direction: Consider the following for the next 04 (four) items that follow:

In an examination of Class XII, $55\%$ of students passed in Biology, $62\%$ passed in Physics, $60\%$ passed in Chemistry, $25\%$ passed in Physics and Biology, $30\%$ passed in Physics and Chemistry, $28\%$ passed in Biology and Chemistry. Only $2\%$ failed in all the subjects.

If the number of students is $360$, then how many passed in at least two subjects?

$ABC$ is a triangle with $AB=1.6 \mathrm{cm}, BC=6.3 \mathrm{cm} \text{and} CA=6.5 \mathrm{cm}$. Let $P \text{and} Q$ be the mid-points of $AB and BC$ Respectively.

What is $A{Q}^2+C{P}^2$ equal to?

Consider the following for the question that follows:

$500$ candidates appeared in an examination comprising tests in English, Hindi and Mathematics. $30$ candidates failed in English only; $75$ failed in Hindi only; $50$ failed in Mathematics only; $15$ failed in both English and Hindi; $17$ failed in both Hindi and Mathematics; $17$ failed in both Mathematics and English; $5$ failed in all three tests.

What is the percentage of candidates who failed in at least two subjects?

In a University there are $1200$ students studying four difference subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

The number of girls studying Statistics is what percent (approximate) of the total number of students studying Chemistry?

Consider the following for the question that follows:

$500$ candidates appeared in an examination comprising tests in English, Hindi and Mathematics. $30$ candidates failed in English only; $75$ failed in Hindi only; $50$ failed in Mathematics only; $15$ failed in both English and Hindi; $17$ failed in both Hindi and Mathematics; $17$ failed in both Mathematics and English; $5$ failed in all three tests.

Direction: Consider the following for the next 04 (four) items that follow:

In an examination of Class XII, $55\%$ of students passed in Biology, $62\%$ passed in Physics, $60\%$ passed in Chemistry, $25\%$ passed in Physics and Biology, $30\%$ passed in Physics and Chemistry, $28\%$ passed in Biology and Chemistry. Only $2\%$ failed in all the subjects.

What is the ratio of number of students who passed in both Physics and Chemistry to number of students who passed in both Biology and Physics but not Chemistry?

$ABC$ is a triangle with $AB=1.6 \mathrm{cm}, BC=6.3 \mathrm{cm} \text{and} CA=6.5 \mathrm{cm}$. Let $P \text{and} Q$ be the mid-points of $AB and BC$ Respectively.

What is $A{B}^2+4B{Q}^2$ equal to?

Direction: Consider the following for the next 04 (four) items that follow:

In an examination of Class XII, $55\%$ of students passed in Biology, $62\%$ passed in Physics, $60\%$ passed in Chemistry, $25\%$ passed in Physics and Biology, $30\%$ passed in Physics and Chemistry, $28\%$ passed in Biology and Chemistry. Only $2\%$ failed in all the subjects.

What percentage of students passed in all three subjects?