Quantitative Aptitude Important Formulas

Height & Distance - Important Formulas,Tricks and Examples

In a right.angled DOAB, where ÐBOA = q,

i)sin q = Perpendicular/Hypotenuse = AB/OB;

ii)cos q = Base/Hypotenuse = OA/OB;

iii)tan q = Perpendicular/Base = AB/OA = sin q/cos q;

iv)cosec q = 1/sin q = OB/AB;

v)sec q = 1/cos q = OB/OA;

vi)cot q = 1/tan q = OA/AB = cos q/sin q.

Trigonometrical identities:

i)sin2q + cos2q = 1.

ii)1+tan2q = sec2q

iii)1+cot2q = cosec2q

Values of T-ratios:-

q

0°

30°

45°

60°

90°

Sin q

0

½

1/Ö2

Ö3/2

1

Cos q

1

Ö3/2

1/Ö2

½

0

Tan q

0

1/Ö3

1

Ö3

Not defined

Angle of Elevation: Suppose a man from a point O looks up an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O, is called the angle of elevation of P as seen from O.

Angle of Depression: Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O, is called the angle of depression of P as seen from O.

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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 ?