# Aptitude & reasoning

## PIPES & CISTERN

Pipes and Cistern   Inlet: A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.   Outlet: A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.   If a pipe can fill a tank in xhours, then: part filled in 1 hour = 1 . x If a pipe can empty a tank in yhours, then: part emptied in 1 hour = 1 . y If a pipe can fill a tank in xhours and another pipe can empty the full tank in y hours (where y > x), ... Read more

## SQUARE ROOT & CUBE ROOTS

Square Root & Cube Root   Step 1: First of all group the number in pairs of 2 starting from the right.   Step 2: To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from left and put the square root of the square.   Step 3: To get the unit’s place digit of the square root   Remember the following If number ends in Unit’s place digit of the square root 1 1 or 9(10-1) 4 2 or 8(10-2) 9 3 or 7(10-3) 6 4or 6(10-4) 5 5 0 0 ... Read more

## SURDS

Surds A surd is a square root which cannot be reduced to a rational number. For example,  is not a surd. However  is a surd. If you use a calculator, you will see that  and we will need to round the answer correct to a few decimal places. This makes it less accurate. If it is left as , then the answer has not been rounded, which keeps it exact. Here are some general rules when simplifying expressions involving surds.       amx an = am + n am = am – n an     (am)n= amn   (ab)n= anbn   a n = an b bn             a0= ... Read more

## SIMPLIFICATION

Simplification Simplification is one of the most important part of Quantitative Aptitude section of any competitive exam. Today I am sharing all the techniques to solve Simplification questions quickly. Rules of Simplification V → Vinculum B → Remove Brackets – in the order ( ) , { }, [ ] O → Of D → Division M → Multiplication A → Addition S → Subtraction   Classification Types Description Natural Numbers: all counting numbers ( 1,2,3,4,5….∞) Whole Numbers: natural number + zero( 0,1,2,3,4,5…∞) Integers: All whole numbers including Negative number + Positive number(∞……-4,-3,-2,-1,0,1,2,3,4,5….∞) Even & Odd Numbers : All whole number divisible by 2 is Even (0,2,4,6,8,10,12…..∞) and which does ... Read more

## PROFIT & LOSS

Profit and 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 Gain = (S.P.) – (C.P.) Loss = (C.P.) – (S.P.) Loss or gain is always reckoned on C.P. Gain Percentage: (Gain %)     Gain ... Read more

## AGE PROBLEMS

Age Problems   Important Formulas on “Problems on Ages”:   If the current age is x, then ntimes the age is nx. If the current age is x, then age nyears later/hence = x+ n. If the current age is x, then age nyears ago = x– n. The ages in a ratio a: bwill be ax and bx. 5. If the current age is x, then 1 of the age is x . n n Example: A problem with one variable: How old is Al? Many single-variable algebra word problems have to do with the relations between different people’s ages. For example: Al’s father is 45. He is 15 years older than twice Al’s age. How ... Read more

## FRACTIONS

Fractions Any unit can be divided into any numbers of equal parts, one or more of this parts is called fraction of that unit. e.g. one-forth (1/4), one-third (1/3), three-seventh (3/7) etc. The lower part indicates the number of equal parts into which the unit is divided, is called denominator. The upper part, which indicates the number of parts taken from the fraction is called the numerator. The numerator and the denominator of a fraction are called its terms. A fraction is unity, when its numerator and denominator are equal. A fraction is equal to zero if its numerator is zero. The denominator of a fraction can never be zero. The value of ... Read more

## DISCOUNT

Discount   The discount is referred to the reduction in the price of some commodity or service. It may anywhere appear in the distribution channel in the form of modifications in marked price (printed on the item) or in retail price (set by retailer usually by pasting a sticker on the item) or in list price (quoted for the buyer). The discount is provided for the purpose of increasing sales, to clear out old stock, to encourage distributors, to reward potential customer etc. In short, the discount can serve as a way to attract customers for a particular item or service. In math, discount is one of the easiest way ... Read more

## PARTNERSHIP

Partnership : Partnership is an association of two or more parties, they put money for business.         Simple Partnership: Simple partnership is one in which the capitals of the partners are invested for the same time. The profit or losses are divided among the partners in the ratio of their investments.         Compound Partnership: Compound Partnership is one which the capitals of the partners are invested for different periods. In such cases equivalent capitals are calculated for a unit time by multiplying the capital with the number of units of time. The profits ... Read more

## Mixed ratio and proportion

Ratio Introduction: Ratio is the relation which one quantity bears to another of the same kind. The ratio of two quantities a and b is the fraction a/b and we write it as a: b. In the ratio a: b, we call a as the first term or antecedent and b, the second term or consequent.   Note: The multiplication or division of each term of a ratio by the same non- zero number does not affect the ratio.   Compound Ratio: – It is obtained by multiplying together the numerators for new numerator and denominators for new denominator.     Example 1. If the ... Read more