FOUNDATION GRADUATES
MODULE 2 : MATHEMATICAL APTITUDE

Time and Distance

This chapter is based on the famous relation: Speed = (Distance/Time). Or the concept of speed as the rate of change of distance

Speed has always been a game changer in the evolution of man from walking on two feet, running as a hunter, and riding a horse to presentday automobiles and airplanes.

The questions can be directly based on a moving object or a system of multiple objects.

Problems based on trains crossing each other and boats travelling in a stream taking the speed of the stream into account with the speed of the boat are common.


Time and Work

This is again a favorite topic for competitive exams.

Here capacity to do work replaces speed in the chapter on Time and Distance.

In Physics, the total work that has to be done is expressed in Joules and the capacity is in Joules/unit time.

Here the total work is taken as 1 and different people with different capacities complete the work

There are three variables in these questions: Part of work done, capacity to do work, and time taken to do the work. When applied to different people, we get the total picture.


Pipes and Cisterns

This can be considered as a subtopic of Time and Work.

In Physics, the number of liters of the cistern is in liters and different pipes have a capacity as the number of liters filled per unit time.

Like in Time and Work, we take to total work to fill the entire cistern as 1 and different pipes filling the cistern in fractions of 1 in unit time.

Here we build equations depending on the number of pipes, capacity in unit time, and time each pipe is operated.


Profit and Loss

This is again a very important topic in competitive exams.

When you are a business owner and you have a product, you buy at a cost price that is fixed and you place it at a fixed marked price.

Now if you sell the item at a selling price of SP above the cost price CP, you're at a profit and the profit percentage is expressed as the difference in SP and CP, at the CP.

Now if you sell the item at SP which is less than CP, you express the difference between CP and SP concerning the transaction as Profit. Profit percentage is expressed again based on the Cost price. We take CP in both cases since it is fixed and not in your control.

Finally, the Marked price, MP is also not in your control and the discount is the difference between MP and SP, it is expressed as a percentage of MP, which is also fixed depending on the market or government regulations.


Simple Interest & Compound Interest

Many people are not comfortable with owning a business, investing in a business, or investing in Stocks. Such people may also lend their money to banks that give an interest, which is less compared to others which can have a risk element.

Now, when the interest for a year is not taken into the next year, we use the formula, which is the simple interest.

Now, in most cases, the interest for a particular year is added to the principal for the next year and this continues until the amount is invested in the bank.

Now the same is true when you borrow money from a bank for different kinds of loans, which includes business loans.


Partnerships

Sometimes there can be multiple owners for a business and each person invests money and time differential basis.

This chapter takes the ratio of products of both time and money for every person to divide the profit.


Races

This chapter is based on two or three people running a race in a circular track and questions are based on their location with time.

Sometimes the tracks can be a square or rectangle and we are interested in the circumference.


Clocks

In a clock, we have three needles to locate the precise time.

Here the relation between time and the angle between the needles is key.

Now in 99% of questions, we deal with only the minute hand and hour hand.


Calendars

Here with the understanding of both a normal year, leap year, and also differential days in months in both years, questions are based on the day of the week for a date and much more.

This can be days in the present and in the future.


Mixtures & Allegations

Now we understand that all solids, liquids, and gases can be homogeneous and heterogeneous.

Homogeneous substances have equal compositions through the substances like water and alcohol and Hetrogeneos substances have nonuniform compositions similar to sand and pebbles, a mix of various dry fruits.

Now in this chapter, we are asked to arrive at a particular ratio of substances for both cases.

Now there are some formulas to arrive at this.
