FORMULA & TRICKS FOR QUANTITATIVE APTITUDE- Part 1Kailasha Foundation

Percentage

To express x% as a fraction, divide it by 100 ⇒ x% = x/100

To express a fraction as %, multiply it by 100 ⇒ x/y = [(x/y) × 100] %

x% of y is given by (y × x/100 )

If X’s age is a% more than Y’s age, the Y’s age is less than X’s age by [ a / (100+a)] * 100%

If ‘M’ is x% of ‘N’ and ‘P’ is y% of ‘N’ then ‘M’ is (x/y) * 100% of ‘P’.

If the sides of the triangle, rectangle, square, circle, rhombus etc is

Increased by a%. Its area is increased by2a+(a²/100)
If decreased b%. Its areas is decreased by,-2b+(b²/100)

The students in a school are ‘P’. It increased by x% during the 1^st year, increased by y% during 2^nd year and again increased by z% during 3^rd year. The students in school after 3 years will be,

P *[(100+x)/100] * [(100+y)/100] * [(100+z)/100]

Problem on Ages

If the current age is x, then n times the age is nx.
If the current age is x, then age n years later/hence = x + n.
If the current age is x, then age n years ago = x – n.
The ages in a ratio a:b ill be ax and bx.
If current age is x, then 1/n of the age is x/n.

If the present age of Sharma Jee is ‘x’ years, then

‘n’ years hence, Age of Sharma Jee would be = (x + n) years

‘n’ years ago, Age of Sharma Jee would be = (x – n) years

Super Tip: You don’t need to always start forming equations from where the question starts.

Number Series

The only difficult part about solving questions on number and alphabet series is determining the pattern. Once you practice 40-50 questions on this topic, you will be aware of 90% of the possible pattern. A shortcut is to read the tricks on solving series questions. Some of them are highlighted here:

Trick 1: Calculate the difference between the immediate or alternate numbers and observe the pattern in the differences.

Trick 2: Observe the sequence for Prime Number series

Trick 3: Observe the sequence for Geometric series, Perfect Squares/Cubes.

Profit & Loss

Cost Price-The price at which an article is purchased is known as cost price (C.P.)

Selling Price-The price at which the article is sold is known as selling price (S.P.)
Profit = SP-CP (SP>CP)
Loss = CP-SP (CP>SP)

Profit % = (Profit x 100)/CP
Loss% = [(CP – SP)/CP] x 100
CP= {100 /(100+profit%)} x SP
CP={100/(100-loss%)} x SP

S.P. = C.P. x [(100 + profit%) / 100]

S.P. = C.P. x [(100 – loss%) / 100]

If there is a Profit of x% and loss of y % in a transaction, then the resultant profit or loss% is given by [x – y – (x × y/100)]

Note- For profit use sign + in previous formula and for loss use – sign. If resultant is positive then overall its profit. However, if it is negative then overall we have a loss.

If a cost price of m articles is equal to the selling Price of n articles,

(C.P of m article = S.P. of n article) then Profit percentage

(m – n)/n×100%

If m parts are sold at x% profit, n parts are sold at y % profit and p parts are sold at z% profit Rs. ‘R’ is earned as overall profit than the value of total consignment
R ×100 / (mx +ny +pz)

Ankit purchases a certain no. of the article at m rupee and the same no. at n a rupee. He mixes them together and sells them at p a rupee then his gain or loss

[{2mn/(m+n)p} -1]× 100

Marked price = Cost price + Markup

Always Remember: Markup is an extra price on Cost Price. So, Markup is always calculated on CP

%Markup = [Markup/CP]*100

Discount (if SP < MP) = MP – SP i.e. SP = MP – Discount

Always Remember: Discount is deducted from Marked Price. So, Discount is always calculated on MP and

%Discount = [Discount/MP]*100

Trick 1: If most of the information given in the form of percentages in the question, start by assuming CP = 100.

Trick 2: Discount is usually given on marked price. Hence, in this case, marked price will be higher than the final selling price.

Simple and Compound Interest

Principal: – The money borrowed or lent out for certain period is called the principal or the Sum.

Interest: – Extra money paid for using other money is called interest

The cost of borrowing money is defined as Simple Interest. It is of two types – simple interest or compound interest. Simple interest (SI) is calculated only on the principal (P) whereas Compound interest (CI) is calculated on the principal and also on the accumulated interest of previous periods i.e. “interest on interest.” This compounding effect makes a big difference in the amount of interest payable on the principal.

Simple interest is:

Simple Interest = Principal x Interest Rate x Term of the loan (Time of Loan)

SI = P x i x n/100 when the interest rate is taken in percent.

Compound Interest

CI = P [(1 + i)ⁿ – 1]

where P = Principal, i = annual interest rate in percentage terms, and n = number of compounding periods.

Compounding periods: When calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest. So for every INR 100 principal over a certain period of time, the amount of interest accrued at 10% annually will be lower than interest accrued at 5% semi-annually, which will, in turn, be lower than interest accrued at 2.5% quarterly.

In the formula for calculating compound interest, the variables “i” and “n” have to be adjusted if the number of compounding periods is more than once a year. That is, “i” has to be divided by the number of compounding periods per year, and “n” has to be multiplied by the number of compounding periods. Therefore, for a 10-year loan at 10%, where interest is compounded semi-annually (number of compounding periods = 2), i = 5% (i.e. 10% / 2) and n = 20 (i.e. 10 x 2).

The following table demonstrates the difference that the number of compounding periods can make over time for an INR 10,000 loan taken for a 10-year period.

Shortcut Trick: Rule of 72

The Rule of 72 calculates the approximate time over which an investment will double at a given rate of return or interest “i”, and is given by (72 / i). It can only be used for annual compounding.

For example, an investment that has a 6% annual rate of return will double in 12 years. An investment with an 9% rate of return will double in 8 years.

Trick 1: Formula for calculating simple interest is simple.

S.I. = PTR/100

What if the rate is R1, R2 and R3 in the 1st, 2nd and 3rd year. In this case, the amount after 3 years would be:

A = P (1 +R1/100) (1 + R2/100) (1 + R3/100)

Trick 2: Formula for calculating compound interest is a little more complex.

A = P [1+ r/100]t

This formula applies when interest is compounded annually.

When interest is compounded half yearly, rate = 2r

compounded quarterly, rate = 4r

compounded monthly, rate = 12r

Trick 3: When the rate of interest is not equal every year:

A = P [1+ r1/100]t1 [1+ r2/100]t2 …. and so on

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