Quantitative Aptitude Important Formulas

Average - Important Formulas,Tricks and Examples

Average
Average = Sum of quantities/ Number of quantities

The average of first n natural numbers is =>[n(n+1)/2] /n => (n +1)/2

Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is = 2xy/(x + y) kmph.

Mean, Median, Mode, and Range

Mean :To find the mean, add all the numbers together then divide by the number of numbers.
The mean is not always a whole number.

Example: Data Set = 2, 5, 9, 7, 5, 4, 3
Number of Elements in Data Set = 7
Mean = ( 2 + 5 + 9 + 7 + 5 + 4 + 3 ) / 7 = 5

Median :To find the median, order the numbers and see which one is in the middle of the list.
If there are two middle values the median is halfway between them. This might not be a whole number.

Example: Odd Number of Elements
Data Set = 2, 5, 9, 7, 5, 4, 3
Reordered = 2, 3, 4, 5, 5, 7, 9 - the middle term is 5
Median = 5

Data Set = 2, 5, 9, 3, 5, 4
Reordered = 2, 3, 4, 5, 5, 9 - the middle terms are 4 and 5
Median = ( 4 + 5 ) / 2 = 4.5 - the median is the average of the two middle terms

Mode :To find the mode, order the numbers lowest to highest and see which number appears the most often.

Example: One Mode
Data Set = 2, 5, 9, 7, 5, 4, 3
Mode = 5

Range :To find the range, subtract the lowest number from the biggest number.

Example:
Data Set = 2, 5, 9, 7, 5, 4, 3
Reordered = 2, 3, 4, 5, 5, 7, 9
Range = ( 9 - 2 ) = 7

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Ratio and Proportion

A certain sum of money is divided between A and B in the ratio of 5/4 : 5/3 and A got Rs. 360/-. Find the total sum of money and B’s share?

In an office, the ratio of the salaries of an officer and a clerk is 15:7. If the salary of a clerk is Rs. 720/- less than the salary of the officer, find the salary of each?

In an election to a municipal council, the votes secured by two candidates are in the ratio 13:19. The elected candidates gets 312 votes more than the second candidate. How many votes are secured by the second candidate?

A certain sum of money is divided between Murthy and Prasad in the ratio 22/7 : 8/3. If Murthy gets Rs. 120/- more than Prasad, find the share of each?

In a cricket test series, the runs made by Raju and Tendulkar are in the ratio 5:9 and Tendulkar and Azar are in the ratio 6:7. What are the runs made by them if Azar makes 187 runs more than Raju?

If A:B = 2:3 and B:C = 9:5 find A:B:C?

If A:B = 3/5:5/7 and B:C = 3/4:2/5, find A:B:C?

If R:S = 0.01:0.11 and S:T = 2.2:1, Find R:S:T?

In a school, Under a Saving Scheme, Rekha saves 3/2 times the savings of Bindu, Geeta saves 4 times the savings of Rekha. Find the ratio of the savings of all the three in least terms?

Simplification

A man left 1/3 rd of his property to his wife and 3/5 th of the remainder to his daughter. He gave the rest to his son who received Rs. 6400/-. How much was his original property worth?

Ratio and Proportion

In a school 4/9 of the pupils are boys. There are 125 girls. How many boys are there?

If A:B = 3:4 and B:C = 5:6, find A:C?

IF X:Y = 3:4 AND Y:Z = 4:5, FIND X:Y:Z?

Area

A house site is in the shape of a square. Its area is 1225 sq metres. What is its perimeter?

The area of a square field is 7396 sq metres. Find its perimeter?

Numbers

Twice the first of three consecutive even integer is 6 more than the second integer. What is the third integers?

Ratio and Proportion

If 2x=3y and 4y=5z, then what is x:z=?

What quantity must be added to each term of the ratio a + b : a – b to make it equal to (a + b)2 : (a – b)2 ?