Quantitative Techniques (Aptitude)

Er. Manit Choudhary B.Tech Mechanical Engineering (2008-12)

M.E. Thermal Engineering (2013-15)

What is Aptitude?

An aptitude is a component of a competency to do a certain kind of work at a certain level, which can also be considered "talent". Aptitudes may be physical or mental.

Aptitudes are natural talents, special abilities for doing, or learning to do, certain kinds of things easily and quickly.

Aptitude Includes:

Vedic Mathematics Number Systems Permutation and Combination Partnership Percentage and Average Problem based on ages Profit and Loss

Simple and Compound Interest Allegation Time, work and Wages Pipes and Cisterns Time and Distance Problem on Train, Boats and Streams Data Sufficiency and Data Analysis Probability Calendar and Clock Number Series Verbal, Non-verbal, Logical and Analytical

Reasoning

Trains Shortcut Methods Points To Remember Time taken by a train of length of L meters to pass a stationary pole

is equal to the time taken by train to cover L meters. Time taken by a train of length of L meters to pass a stationary

object of length P meters is equal to the time taken by train to cover (L + P) meters.

If two trains are moving in same direction and their speeds are x km/h and y km/h (x > y) then their relative speed is (x y) km/h.

If two trains are moving in opposite direction and their speeds are x km/h and y km/h then their relative speed is (x + y) km/h.

Unit Conversion

Some Shortcut Methods Rule 1:

If two trains of p meters and q meters are moving in same direction at the speed of x m/s and y m/s (x > y) respectively then time taken by the faster train to overtake slower train is given by

Rule 2:

If two trains of p meters and q meters are moving in opposite direction at the speed of x m/s and y m/s respectively then time taken by trains to cross each other is given by

Percentage:- Percentage Increase/Decrease: If the price of a commodity increases by R%, then the reduction in

consumption so as not to increase the expenditure is: If the price of a commodity decreases by R%, then the increase in consumption

so as not to decrease the expenditure is:

Results on Population: Let the population of a town be P now and suppose it increases at the rate of

R% per annum, then: 1. Population after n years =

2. Population n years ago =

%100100

R

R

%100100

R

R

nRP

100

1

nRP

1001

Results on Depreciation: Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then: 1. Value of the machine after n years =

2. Value of the machine n years ago =

nRP

100

1

nRP

1001

Profit & Loss IMPORTANT FACTS Cost Price: The price, at which an article is purchased, is called its cost price,

abbreviated as C.P. Selling Price: The price, at which an article is sold, is called its selling prices, abbreviated

as S.P. Profit or Gain: If S.P. is greater than C.P., the seller is said to have a profit or gain. Loss: If S.P. is less than C.P., the seller is said to have incurred a loss.

IMPORTANT FORMULAE (a) Gain = (S.P.) - (C.P.) (b) Loss = (C.P.) - (S.P.) (c) Loss or gain is always reckoned on C.P. (d) Gain Percentage: (Gain %) Gain % = (e) Loss Percentage: (Loss %) Loss % = (f) Selling Price: (S.P.) SP = OR (g) Cost Price: (C.P.) CP = OR

..100

PCGain

..100

PCLoss

..100

%100 PCGain

..100

%100 PCLoss

..%100

100 PSGain

..%100

100 PSLoss

Partnership: When two or more than two persons run a business jointly, they are called

partners and the deal is known as partnership. Ratio of Divisions of Gains:

When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.

Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:

(A's share of profit) : (B's share of profit) = x : y. When investments are for different time periods, then equivalent

capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.

Suppose A invests Rs. x for p months and B invests Rs. y for q months then,

(A's share of profit) : (B's share of profit)= xp : yq.