# Shortcut Tricks to Solve - Ratio and Proportion

## SHORTCUT RULES TO SOLVE PROBLEMS ON RATIO AND PROPORTION

### Effective for IBPS PO - SBI PO Exam

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. 