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**If you take more than 5 seconds to solve Ratio and Proportion Problems, then this post is for you because this smart method does not even use the Ratio and Proportion Formulas! **

Amongst all the problems that are asked in the quantitative aptitude section of IBPS PO Exam, Ratio and Proportion Problems are the easiest. But the long list of Ratio and Proportion Formulas and the copious amount of calculations needed, often makes them tedious.

In the 20th Smart Method in this series of blog posts we will discuss a trick that will help you solve ratio and proportion problems without using the long list of ratio and proportion formulas, that too in only 5 seconds!

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**Ratio and Proportion**

Ratio is a relationship between two numbers indicating how many times the first number contains the second. Proportion is a name we give to a statement where two ratios are equated with each other.

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**Ratio and Proportion Formulas**

1. Ratio: The ratio of two quantities

*a*and*b*in the same units, is the fraction a/b and we write it as*a*:*b*.
In the ratio

*a*:*b*, we call*a*as the first term or antecedent and b, the second term or consequent.
Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

2. Proportion: The equality of two ratios is called proportion.

If *a* : *b* = *c* : *d*, we write *a* : *b* :: *c* : *d* and we say that *a, b, c, d* are in proportion.

Here

*a*and*d*are called extremes, while*b*and*c*are called mean terms.
Product of means = Product of extremes.

Thus,

*a*:*b*::*c*:*d*<=> (*b*x*c*) = (*a*x*d*)###
**Example of Ratio and Proportion Problems**

A sum of money is divided among A, B, C and D ratio 3:5:8:9 respectively. If the share of D is 1872 more than the share of A, then what is the total amount of money of B & C together?

1) 4156 2) 4165 3) 4056 4) 4065 5) None of these

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**Conventional Method to Solve Ratio and Proportion Problems**

The school book approach to this question uses the ratio and proportion formulas and starts with assuming T (or any other variable) as the total and then dividing it based on the relative division of the quantity between the quantities.

Let the total amount be ‘T’

**Step 1:**

A’s share= (3/25)T, B’s share= (5/25)T, C’s share= (8/25)T, D’s share= (9/25)T

**Step 2:**

D = A + 1872

**Step 3:**

(9/25)T = (3/25)T + 1872

**Step 4:**

(6/25)T = 1872

**Step 5:**

T = 1872 x (25/6)= 7800

**Step 6:**

B + C = (5/25)T + (8/25)T

**Step 7:**

B + C = (13/25)x 7800

**Step 8:**

B + C= 4056

Phew! Finally the correct answer after so many steps…

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**Smart Method to Solve Ratio and Proportion Problems**

The above method may lead you to the correct answer but it’s a bad idea to use it in exams where time is not your friend! A smart method is one which

*eliminates all extra calculations and steps.*
We know that

A’s share= 3 parts, B’s share= 5 parts, C’s share= 8 parts, D’s share= 9 parts

**Step 1:**

Also we know D- A= 1872= 9 parts – 3 parts= 6 parts= 1872

**Step 2:**

B + C = 13 parts

**Step 3:**

On Cross Multiplication we get B + C = 13 x (1872/6) = 4056

*Rather than first get the value of whole, establish a relationship between the given ratios and eliminate all redundant steps and calculations.*
Watch our expert faculty explain this smart method.

Try solving these ratio and proportion problems sans the ratio and proportion formulas to get the correct answer!

Question 1: A sum of money is divided among A, B, C and D in the ratio 5:8:9:11. If the share of B is 2475 more than the share of A, then what is the total amount of money of A & C together?

1) 9900 2) 11550 3) 10725 4) 9075 5) None of these

Question 2: A sum of money is divided among P, Q, R and S in the ratio 6:9:8:10. If the share of Q is 2463 more than the share of P, then what is the total amount of money of P & R together?

1) 9963 2) 11494 3) 10725 4) 9075 5) None of these

Do write your answer in the comments section below and tell us in exactly how many seconds you solved these ratio and proportion problems.

Stay tuned to this space for more and till then keep practicing with smart methods!

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