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## Ratio and Proportion Questions for SSC

Nov 28 • quantitative aptitude questions, SSC Exam • 1808 Views • No Comments on Ratio and Proportion Questions for SSC

# 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

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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

 Short tricks 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 Share of A = R/m  + n × m Share of B = R/m  + n × n Difference between the share of A and B = R/m  + n × (m – n) Following Question Prepared by Best Bank Coaching in Noida 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 Numbers of coin x = m/xm + yn + zr × R Numbers of coin y = n/xm + yn + zr × R Numbers of coin z = r/xm + yn + zr × R
 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

 If in a X liter mixture of milk and water, the quantity of milk is m%, then how many liters of milk should be added to the mixture such that the quantity of milk increase to n % = X(n – m)/100 – n If in a X liter mixture of milk and water, the quantity of milk is m%, then how many liters of water should be decreased or vaporized from the mixture such that the quantity of milk increase to n % = X(m – n)/100 – n A container contains X liters of water. If m liters of water is replaced by m liters of milk and this process is repeated n times , then the quantity of water in the new mixture is                   X (1 – m/x)n If by selling mixture of milk and water on the cost price of milk there is a profit of m%, then the ratio of milk and water = 100 : r

Partnership

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