## SHORTCUT RULES TO SOLVE PROBLEMS ON RATIO AND PROPORTION

### Effective for IBPS PO - SBI PO Exam

**Dear Reader,**

Here we will start a series of Quantitative Aptitude Shortcut Tricks for your upcoming SBI - IBPS - SSC and Other Government Competitive Exams. We will try to cover up all topics of the quantitative Aptitude Sections from which question was generally asked.

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**Trick - 1**

- If two numbers are in the ratio of a:b and the sum of these numbers is x, then these numbers will be
**ax/a+b**and**bx/a+b**respectively.

**Trick - 2**

- To find the number of coins, Number of each types of coin = Amount in rupees / value of coins in rupees

**Tricks -3**

- The contents of two vessels containing water and milk are in the ratio x1:y1 and x2:y2 are mixed in the ratio x:y. The resulting mixture will have water and milk in the ratio of

$x{{x}_{1}}({{x}_{2}}+{{y}_{2}})+y{{x}_{2}}\left(
{{x}_{1}}+{{y}_{1}} \right):x{{y}_{1}}\left( {{x}_{2}}+{{y}_{2}}
\right)+y{{y}_{2}}\left( {{x}_{1}}+{{y}_{1}} \right)$

**Trick - 4**

- If three numbers are in the ratio of
**a:b:c**, and sum of these numbers is x, then these numbers will be**ax/a+b+c**,**bx/a+b+c**, and**cx/a+b+c**respectively.

**Trick -5**

- To find the strength of milk, Strength of milk in the mixture = Quantity of Milk / Total Quantity of Mixture

**Trick -6**

- If in a mixture of x liters, milk and water are in the ratio of a:b, then the quantities of milk and water in the mixture will be ax/a+b liters and bx/a+b liters respectively.

**Trick - 7**

- The ratio between two numbers is a:b. If each number be decreased by x, the ratio becomes c:d. Then sum of the two numbers

$=\frac{x\left(
a+b \right)\left( d-c \right)}{ad-bc}$

**Questions for Practice****Q1. Two numbers are in the ratio of 3;1. If sum of these two numbers is 440, find the numbers.**

**Q2. A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is Rs.35, how many coins of each type are there?**

**Q3. The contents of two vessels containing water and milk are in the ratio 1:2 and 2:5 are mixed in the ratio 1:4. The resulting mixture will have water and milk in the ratio.**

**Q4. An amount of Rs.750 is distributed among A, B and C in the ratio of 4:5:6. What is the share of B?**

**Q5. One man adds 3 liters of water to 12 liters of milk and another 4 liters of water to 10 liters of milk. What is the ratio of the strengths of milk in the two mixtures**

**Q6. In a mixture of 65 liters milk and water are in the ratio of 3:2 . What the quantities of milk and water in the mixture?**

**Q7. The ratio of two numbers is 7:9. If each number is decreased by 2, the ratio becomes 3:4. Find the sum of the two numbers.**

__Answers__**Answer 1. 110**

**Answer 2. 20**

**Answer 3. 31:74**

**Answer 4. 250**

**Answer 5. 28:25**

**Answer 6. 26**

**Answer 7. 32**

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