Smart Tricks to Solve Partnership, Ratio and Proportion Questions

Smart Tips for Partnership, Ratio & Proportion for Bank PO

Candidates consider Quantitative Aptitude as one of the difficult and core subject for any banking exams. This sections if practised well can be easy or may shock you anytime by raising the difficulty level. You can also check out  Quantitative Aptitude Quiz.


We have already shared the study plan for IBPS PO in the form of KAR IBPS PO FATEH! and providing the daily quiz on the basis of the Study plan. Now we have also started a new initiative of Study notes. Today we are discussing the Partnership, Ratio & Proportion for Bank PO.

Ratio & Proportion

→ Ratio of two Quantities is the number of times one quantity contains another quantity of same type.
→ The ratio between a and b can be represented as a : b, where a is called antecedent and b is called consequent.
i.e  a/b or a : b
→ Different types of ratio are explained as below:-
(1) Duplicate Ratio :- If the numbers given are in ratio, then the ratio of their squares is called duplicate ratio.
For ex. 2:3=4:9
(2) Sub-Duplicate Ratio:- If given two numbers are in ratio, then ratio of their square roots is called sub-duplicate ratio 
For ex 25 : 36 = 5 : 6
(3) Triplicate Ratio:- If the given numbers are in ratio, then ratio of their cubes is called triplicate ratio
For ex- 4 : 5 = 64 : 125
(4) Sub- triplicate Ratio:- If the given numbers are in ratio, then ratio of their cube roots is called sub-triplicate ratio
For ex- 125 : 343 = 5 : 7
(5) Inverse Ratio:- If given numbers are in ratio then their antecedent and consequent are interchanged and the ratio obtained is called inverse ratio
* Proportion:– An equality of two ratios is called the proportion.
→ If L/M=x/y or L : M = x : y, then we can say that L, M, x, y are in proportion and can be written as L : M :: x : y
Some important rules of proportion:-
Rule 1:- If x : y :: y : z, then z is called third proportional to x and y
x : y ∷ y : z ⇒ x : y = y : z
⇒ x × z = y × y
⇒ y² = xz
Rule 2:- If L : M :: x : y, then y is called the 4th proportional to L, M and x, y
i.e L : M ∷ x : y
⇒ L : M = x : y
⇒ L × y = Mx

Some examples are as follow:-

Ex) calculate 3rd proportional of 18 and 36 Let 3rd proportion be x
18 : 36 ∷ 36 : x
Let mean proportion be x
Then 18 : x ∷ x : 8
⇒ x² = 144
⇒ x = 12
* Some important rules of ratio:-
Rule 1:- If two given ratio are l : m and x : y, then
(i) l : m > x : y if ly > mx
(ii) l : m < x : y, if ly < mx
(iii) l : m = x : y, if ly = mx

Rule 2:- If two ratios are given, convert each ratio in such a way that both ratios have same denominator, then compare their numerators, the fractions with greater numerator will be greater

Ex) Divide 1150 in the ratio 14 : 9
→ Let 1st part be 14x and 2nd part be 9x
∴ 14x + 9x = 1150
23x = 1150
∴ x = 50
∴ 1st part = 14x = 700
2nd part = 9x = 450

(Ex) The ratio of income of manan and Aman is in ratio 2 : 3 and their expenditure is in ratio 7 : 12.  If each of then saves 3000 Rs, then find their income and expenditure?
→ Let income of manan and Aman be 2x and 3x
 expenditure of manan = (2x – 300) Rs
expenditure of Aman = (3x – 3000) Rs
income of manan = 2x = 10000 Rs
income of Aman = 3x = 15000 Rs
and expenditure of manan = 10000 – 3000 = 7000 Rs
expenditure of Aman =  15000 – 3000 = 12000 Rs
Ex) If two numbers are in ratio 3 : 4. If 15 is added to both the numbers, then the ratio becomes 7 : 9. Find the greatest number?
Let the two numbers be 3x and 4x
∴ 9(3x + 15) = 7 (4x + 15)
∴ 27x + 135 = 28x + 105
∴ x = 30
∴ greater number = 4x
= 120
* Faster approach:-

Here x =3, y = 4, m = 7, n = 9 and a = 15
∴ Two numbers are
* Type 4:- Two numbers are in ratio x : y and a is subtracted from the numbers, then the ratio becomes m : n. The two numbers will be

Partnership


→ When two or more persons makes a group and invest money for running a certain business and after certain time receive profit in the ratio of their invested money and time period, then such a group is called partnership
→ It is of 2 types:-
(1) Simple partnership:- If all partners invest their different capitals for the same time period or some capital for different time period.
(2) Compound partnership:- If all partners invest their different capitals for different time period.
* Partners are also of 2 types:-
(1) Working partner:- A partner who not only invests money, but also takes part in business activities and gets some salary for that
(2) Sleeping partner:- A partner who only invests money, and not take part in business activities
Ex) P and Q starts a business by investing 6000 Rs and 9000 Rs respectively. Find the ratio of their profit after 1 yrs?
Ex) A start a business with 6000 rs and B joins the business 5 month later with 8000 rs. Find the share of A and B if total profit is 16000 Rs after 1 year?
    A      :     B
6000        8000
× 12          × 7
  72             56
∴ 18         14
∴ 9           7
∴ A’s share = 16000 × 9/16 = 9000 rs
B’s share = 16000 × 7/16 = 7000 rs
→ Different types of  questions asked nowadays in the exams are as follow:-
Type 1:- If a : b : c is the ratio of investment and x : y : z is the ratio of profits, then the ratio of time period of investment is given by


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