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**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.

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**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.

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.

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**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

**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

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**(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

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**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

**You may also like to Read:**

**Quantitative Aptitude Study Notes for Bank Exams****Quantitative Aptitude Questions for all Competitive Exams**