What is Ratio?
A ratio is a relationship between two numbers by division of the same kind. The ration of a to b is written as a : b = a / b In ratio a : b , we can say that a as the first term or antecedent and b, the second term or consequent.
Example : The ratio 4 : 9 we can represent as 4 / 9 after this 4 is a antecedent and , consequent = 9
Rule of ration : In ratio multiplication or division of each and every term of a ratio by the same non- zero number does not affect the ratio.
What is Proportion?
The idea of proportions is that two ratio are equal.
If a : b = c : d, we write a : b : : c : d,
Ex. 3 / 15 = 1 / 5
a and d called extremes, where as b and c called mean terms.
Proportion of quantities
the four quantities a, b, c, d said proportion then we can express it a : b = c : d
Then a : b : : c : d <–> ( a x d ) = ( b x c ) product of means = product of extremes.
If there is given three quantities like a, b, c of same kind then then we can say it proportion of continued.
a : b = b : c the middle number b is called mean proportion. a and c are called extreme numbers.
So, b^{2} = ac. ( middle number )^{2} = ( First number x Last number ).
Quiz on ratio and proportion:-
1 If P : Q : R = 2 : 3 : 4 , Then P / Q : Q / R : R / P = ?
A. 8: 9: 24 B. 7: 9: 24 C. 4: 6: 15 D. 8: 11: 24 E. None of these
2: If 2P = 3Q = 4R, Then P : Q : R = ?
A. 2: 3: 5 B. 2: 3: 4 C. 3: 5: 6 D. 1: 2: 3 E. None of these
3: If P : Q = 2 : 3 , Q : R = 4 : 5 and R : S = 6 : 7 , then P : S = ?
A. 18: 25 B. 17: 35 C. 16: 35 D. 8: 11 E. None of these
4:Rama distributes his pencil among his four friends Rakesh, Rahul, Ranjan, and Rohit in the ratio 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 . What is the minimum number of pencils that the person should have?
A. 66 B. 64 C. 72 D. 77 E. None of these
5: Two numbers are respectively 40% and 60% more than third number. Find the ration of two numbers ?
A. 8: 7 B. 7: 9 C. 9: 11 D. 8: 13 E. None of these
Answers with Explanation:-
1. P : Q : R = 2 : 3 : 4 .
Let P = 2k,
Q = 3k,
R = 4k.
Then,
P / Q = 2k / 3k = 2 / 3 ,
Q / R = 3k / 4k = 3 / 4
R / P = 4k / 2k = 2 / 1.
2. Let 2P = 3Q = 4R = k ,
Then ,
P = k / 2,
Q = k / 3 ,
R = k / 4.
SO , P : Q : R = k / 2 : k / 3 : k / 4 = 6 : 4 : 3.
3. (C)
4. Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
5.Step 1: Let the third number is A
Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.
Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.