Aptitude Practice

Point to remember: Time taken by a train x metres long in passing a signal post or a pole or a standing man is equal to the time taken by the train to cover x metres. Time taken by a train x metres long in passing a stationary object of length y metres is equal to the time taken by the train to cover x+y metres. Suppose two trains are moving in the same direction at u kmph and v kmph such that u>v, then their relative speed = u-v kmph. If two trains of length x km and y km are moving in the same direction at u kmph and v kmph, where u>v, then time taken by the faster train to cross the slower train = (x+y)/(u-v) hours.  Suppose two trains are moving in opposite directions at u kmph and v kmph. Then, their relative speed = (u+v) kmph.  If two trains of length x km and y km are moving in the opposite directions at u kmph and v kmph, then time taken by the trains to cross each other = (x+y)/(u+v)hours.  If two trains start at the same time from two points A and B towar...

The ratio a : b represents a fraction a/b.  a is called antecedent and b is called consequent.  The equality of two different ratios is called proportion.  If a : b = c : d then a, b, c, d are in proportion.  This is represented by a : b :: c : d. In a : b = c : d, then we have a* d = b * c.  If a/b = c/d then ( a + b ) / ( a – b ) = ( d + c ) / ( d – c ). Equivalent Ratios  Let us divide a Pizza into 8 equal parts and share it between Ram and Sam in the ratio 2:6. The ratio 2:6 can be written as 2/6;2/6 = 1/3 We know that 2/6 and 1/3 are called equivalent fractions. Similarly we call the ratios 2:6 and 1:3 as equivalent ratios. From a given ratio x : y, we can get equivalent ratios by multiplying the terms ‘x’ and ‘ y ‘by the same non-zero number. For example 1 : 3 = 2 : 6 = 3 : 9 4 : 5 = 12 : 15 = 16 : 20 Ratio and Proportion Problems and Solutions Example 1:  Write any 4 equivalent ratios for 4 : 3. Sol:  Given Ratio = 4 : 3. The ratio in fract...

Formulae:- Gain = Selling Price(S.P.) - Cost Price(C.P)  Loss = Cost Price (C.P.) - Selling Price (S.P) Gain % = Gain x 100 / C.P. Loss % = Loss x 100 / C.P  S.P. = [(100 + Gain%)/100] x C.P  S.P. = [(100 - Loss%)/100] x C.P  C.P. = [100/ (100 + Gain%) ] x S.P  C.P. = [100/ (100 - Loss%) ] x S.P  When a person sell two similar items , one at a gain of say x% , and other at a loss of x% then the seller always incure a loss given by - Loss % = ( Common loss & gain % / 10 )2  If a trader professes to sell his goods at cost price , but uses false weight , then Gain% = [ Error / (True value – Error ) ] x 100 % TRUE DISCOUNT  Ex. Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum.  Clearly, Rs. 100 at 14% will amount to R. 156 in 4 years. So, the payment of Rs. now will clear off the debt of Rs. 156 due 4 years hence. We say that: Sum due = Rs. 156 due 4 years  hence: Present Worth (P.W.) = Rs. 100;...

If A can do a piece of work in n days, then A's 1 day's work = 1/n  If A and B work together for n days, then (A+B)'s 1 days's work = 1/n  If A is twice as good workman as B, then ratio of work done by A and B = 2:1  Basic Formula : If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then  M1 D1 H1 / W1 = M2 D2 H2 / W2  If A can do a piece of work in p days and B can do the same in q days,  A and B together can finish it in pq / (p+q) days. Illustration 1:   Samir can do a job in 30 days. In how many days can he complete 70% of the job? Sol:  Now as per the question he finishes the work in 30 days, or he can do 100% of the work in 30 days. If he has to do only 70% of the work, he will require 70% of the time.  Number of days required = 30 × 70/100 = 21 days. Illustration 2:   Reshma can do 75% job in 45 days. In how many days ca...

Types of Numbers Natural Numbers:  The numbers 1,2,3,4.... are called natural numbers or positive integers. Whole Numbers:  The numbers 0,1,2,3.... are called whole numbers. Whole numbers include “0”. Integers:  The numbers .... -3, -2, -1, 0, 1, 2, 3,.... are called integers. You will see questions on integers in almost all the exams where you see number system aptitude questions. Negative Integers:  The numbers -1, -2, -3, ... are called negative integers. Positive Fractions:  The numbers(2/3) ,(4/5) ,(7/8) ... are called positive fractions. Negative Fractions:  The numbers -(6/8) ,-(7/19) , -(12/17) ... are called negative fractions. Rational Numbers:  Any number which is a positive or negative integer or fraction, or zero is called a rational number. A rational number is one which can be expressed in the following format ⇒(a/b) , where b ≠ 0 and a & b are positive or negative integers. Irrational Numbers:  An infinite non-recurring decimal...

Greatest Common Divisor (GCD)/ Highest Common Factor (HCF) The highest common factor of two or more numbers is the greatest common divisor, which divides each of those numbers an exact number of times. The process to find the HCF is Express the numbers given as a product of prime numbers separately i.e. finds factors of numbers Take the product of prime numbers common to both numbers Illustration 1: Find the HCF of 1728 and 14. Sol: The prime factorization of 1728 is 12 × 12× 12= 3 3 x2 6 . The prime factorization of 14 is 2 × 7. The common prime factor is 2. HCF = 2. Illustration 2: Find the HCF of 27, 18 and 36. Sol: Firstly find the prime factors of the numbers such as 27 = 3 × 3 × 3, 18 = 3 × 3 × 2 and 36 = 3 × 3 × 2 × 2, then take the common prime numbers, which are 3 & 3. Now the product of these prime numbers i.e. 3 × 3 = 9 is the HCF of these two numbers. Understanding LCM or Least Common Multiple The least common multiple (LCM) of two or more numbers is the smallest of the...