Ratio and Proportion Questions for SSC
Ratio and Proportion Questions for SSC CGL BANK POO SO and other government exam.
Ratio : The ratio of a to b is a fraction a/b and is written as a:b
Note: the value of ratio remains same if we multiply or divide the numerator and denominator of a fraction by the same number.
a : b = a/b = am/bm = a : b or
A : b = a/b = a/mb/m = a/m
Compounded ratio : If two or more ratios are multiplied term by term i.e the numerator to numerator and denominator to denominator, the ratio thus obtained is called their compounded ratio
Example the compounded ratio of a : b and c : d is ac : bd
Duplicate ratio : the duplicate ratio of a : b is a^2 : b^2
Example the duplicate ratio of 2 : 3 = 4 : 9
Triplicate ratio : the triplicate ratio of a : b is a^3 : b^3
Sub-duplicate ratio : the sub-duplicate ratio of a : b is a^½ : b^½
Sub triplicate ratio : the sub triplicate ratio of a : b is a^⅓ : b^⅓
Reciprocal or inverse ratio : the inverse ratio of a : b is 1/a : 1/b which is same as b : a
Proportion : if two ratios are equal, then they are said to be in proportion
Example : consider 2 : 5 and 4 : 10 , since 2/5 = 4/10 , hence 2,5,4 and 10
are in proportion and can be written as 2 : 5 : : 4 : 10
In the proportion 2 : 5 : : 4 : 10, the end terms 2 and 10 are called extremes and the middle terms 5 and 4 are called means.
Product of extremes = product of means
Continued proportion and third proportion : If a/b = b/c , then a, b, and c are said to be in continued proportion and c is called the third proportion. The third proportion of a and b is b^2 / a.
Fourth proportion : if a, b, c and d are in proportion then d is called the fourth proportion. The fourth proportion of a, b and c is bc / a .
Mean proportion : mean proportion of two numbers a and b is √ab
1. If A : B : C = a : b : c
Then A/B : B/C : C/A = a2 c : b2 a : c2 a
2. If A : B = a : b, B : C = b : c, C : D = c :d
Then A : C = a : c, A : D = a : d and B : D = b : d
3. If a sum of money R is divided in A and B in the ratio m : n, then
4. If a bag contain the coins of Rs. x, Rs. y and Rs. z in the ratio of m : n : r and the total value of the coins is Rs. R, then
|5. In a glass, the ratio of the mixture of milk and water is m : n and in another glass of same quantity of mixture is p : q. If the mixture of these two glasses mix up in a third glass, then the ratio of milk and water will be
= (m/m + n + p/p + q) : (n/m + n + q/p + q)
|6. In X lite mixture, the ratio of water and milk is p : q. How many liters of water should be added to this mixture so that the ratio will become r : s.
= X(ps – qr)r/(p + q)
Allegation and mixture
Allegation rule : The two ingredients should be mixed in the inverse ratio of the differences of the two given prices and the mean price i.e.
(Quantity of cheaper product / quantity of dearer product ) = (Cost price of dearer – mean price) /
(mean price – cost price of cheaper)
Note : C.P. of unit quantity of the mixture is called the mean price.
We represent it as
Cheaper quantity : dearer quantity = (d – m) : (m – c)
Short tricks on allegation and mixture
X (1 – m/x)n
Partnership : To solve the problems involving partnership , use this trick
(A’s capital × A’s time in partnership)/(B’s capital × B’s time in partnership) = A’s profit/B’s profit
For three persons A, B and C
(A’s capital × A’s time) : (B’s capital × B’s time ) : (C’s capital × C’s time ) =
A’s profit : B’s profit : C’s profit