# Percentages for Competitive Exams

Percentages for Competitive Exams is an essential topic. A Fraction whose denominator is 100 is called Percentage. As we all know Cent means 100, So percentage means for each value of 100.

Percentage based problems are asked in every exam whether it is UPSC, TEACHING, INSURANCE, UGC, SSC, BANKING, RBI, SBI, NABARD, IBPS, DEFENCE, RAILWAY or Other state-based exams.

To solve percentage-based question easily and quickly we have provided you some important percentage in fraction form. With the help of their fraction form it will become easy for candidates to solve questions in fraction of seconds.

## Fractional value for some Percentages for Competitive Exams to do fast calculation.

1 = 100%

½ = 50%

1/3 =33.33 = 33 ½ %

¼ = 25%

1/5 = 20%

1/6 = 16.66% = 16 2/3 %

1/7 = 14.28% = 14 2 /7%

1/8 = 12.5% = 12 1/8 %

1/9 = 11.11% = 11 1/9%

1/10 = 10%

1/11 = 9.09% = 9 1/11%

1/12 = 8.33% = 8 1/3 %

1/13 = 7.69% = 7 9/13%

1/14 = 7.14% = 7 1/7%

1/15 = 6.66% = 6 2/3%

1/16 = 6.25% = 6 ¼%

1/17 = 5.88% = 5 15/17%

1/18 = 5.55% = 5 5/9%

1/19 = 5.26% = 5 5/19%

1/20 = 5%

### Some more, "Repeatedly asked" Fractional Value of Percentage.

3/8 = 37.5%

5/8 = 62.5%

7/8 = 87.5%

2/3 = 66.66%

7/16 = 43.75%

9/16 = 56.25%

5/7 = 71 3/7 = 71.42%

2/7 = 28 4/7% = 28.57%

4/7 = 57 1/7% = 57.14%

5/6 = 83 1/3% = 83.33%

5/4 = 125%

3/2 = 150%

2/3 = 66.66 = 66 2/3%

**Percentage Tricks:**

A simple but a very useful trick is given just below it. It will be helpful in solving questions related to Percentages for Competitive Exams.

**x % of y = y % of x**

For example : If you need to calculate 87.5% of 80 then you can calculate 80% of 87.5, both will be equal.

Prove 87.5% of 80 = 70

or 80% of 87.5 = 70

##### Related Formulae for Percentages for Competitive Exams are given below. For fast calculation learn them by heart.

**1. To calculate the percentage of a fraction we have to use the given formula.**

**Percentage formula = (Numerator/Denominator) ×100**

**For example:** To Calculate Percentage form of 5/8, we need to multiple the Numerator by 100 and then will have to divide the resultant by Denominator.

5/8*100 = 5*100/8 = 500/8 = 62.5%

**2. To calculate the percentage of a Number.**

**Percentage /100* Number**

To calculate the Percentage of a number, First multiple the number with the required percentage and the divide the result by 100.

**For example:** Calculate 15% of 60?

P*Number/100 = 15*60/100 =900/100 = 9.

**3. To express x% as a fraction.**

**X%/100**

To express % as a Fraction, we need to just divide it by 100.

**For Example** : 35% as Fraction

35/100 = 7/20

**4. To Increase A value or Number by Given Percentage.**

**Number * 100+x%/100**

If you want to Increase the Number by given percentage then you have to multiple the Number by sum of that given percentage and 100 and then divide the result by 100.

**For example** : Increase 500 by 30%

500*100+30/100 = 500*130/100 = 65000/100 =650.

**5. To Decrease A value or Number by Given Percentage.**

**Number * 100-x%/100**

If you want to decrease the Number by given percentage then you have to multiple the Number by difference of that given percentage and 100 and then divide the result by 100.

**For example** : Decrease 500 by 30%

500*100-30/100 = 500*70/100 = 35000/100 =350.

**6. To calculate the percentage ****Decreament ****of a number.**

**Percentage Decreament = Initial value-Final value/ Initial value*100**

To calculate the Percentage decreament of a number, you have to first find the difference between initial and final value and then divide the result by initial value and then divide the result so obtained by 100.

**For example** : Cost of toy car decrease from 800 to 500, calculate the percentage decreament happened?

= 800-500/800*100 = 300/800*100 = 30000/800 = 37.5%

**7. To calculate the percentage increament of a number.**

**Percentage Increament = Final value – Initial value/ Initial value*100**

To calculate the Percentage Increament of a number, you have to first find the difference between final and initial value and then divide the result by initial value and then divide the result so obtained by 100.

**For example** : Cost of toy car increase from 500 to 800, calculate the percentage increament happened?

= 800-500/500*100 = 300/500*100 = 30000/500 = 60%

**8. If X% of A is equals to Y% of B.**

**Z% of A = y*z/x% of B**

**For example** : If 20% of A is equal to 15% of B, Then find 10% of A is equal to what Percent of B?

10% of A = 15*10/20% of B

10% of A = 7.5% of B.

**9. If the passing marks in an examination is P%. If a candidate scores S marks and fails by F marks then Maximum Marks will be.**

**Maximum Marks = 100*P+S/P**

**For example** : Prem Kumar has to score 28% marks to get through. If he gets 40 marks and fails by 50, then find the total marks set for the examination?

Maximum Marks = 100*40+50/40 = 100*90/40 = 9000/40 =225

**10. If a candidate scores marks and fails by A marks while an another candidate scores y% marks and gets B marks more than minimum passing marks, then Maximum Marks will be**.

**Maximum Marks = Sum of score *100/Difference in % Marks**

**For example** : Aashish scores 20% and fails by 80 marks, while Rohan who scores 60% marks, gets 40 marks more than the minimum required marks to pass the examination. Find the maximum marks for the examination?

Maximum Marks = 80+40/60-20*100 = 120*100/40 = 12000/40 = 300.

**11.If the price of an item decreases, a person can buy few Kg more in Y rupees, then actual price of that item.**

**Actual Price = Rate * Y/100- Rate*X Per Kg**

Radha can buy 5 Kg more apples in rupees 100 as the price of apples has decreased by 10%. Find the actual price of the apples?

Actual Price = 10*100/100-5 *5 = 1000/95 *5 = 1000/475 = 2 2/9 per kg

**12. If the population of a town is P and it increases at the rate of R% per annum then –Population after ‘n’ years** :

**Percentage population = P x (1 + R/100) ^{n}**

**13. If the population of a town is P and it decreases at the rate of R% per annum then –Population after ‘n’ years** :

**Percentage population = P x (1 – R/100) ^{n}**

**14. If the population of a town is P and it increases at the rate of R% per annum then –Population of the town ‘n’ years ago :**

** Population n years ago = P/(1 + R/100) ^{n}**

**15. If the population of a town is P and it decreases at the rate of R% per annum then –Population of the town ‘n’ years ago:**

**Population n years ago = P/(1 – R/100) ^{n}**

**16.Cost of Machine**

**Value of Machine After n years = P x (1 – R/100) ^{n}**

**Value of Machine Before n years = P/(1 – R/100) ^{n}**

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