**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Percentage**

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**Percent**

The meaning of the term per cent is ‘for every hundred’. It can be defined as follows. “A per cent is a fraction whose denominator is 100 and the numerator of the fraction is called the rate per cent”, per cent is denoted by the sign “%”.

**Formula to Calculate Per cent**

If we have to find y% of x, then

y% of x = x X y/100

**Some Basic Formulae (or Key Facts)**

- To find how much per cent one quantity is of another. Required percentage

**Example 1.14 expressed as a per cent of 1.9 is SSC (10 + 2) 2010**

(a) 6%

(b) 10%

(c) 60%

(d) 90%

- When a number x is increased or decreased by y%, then the new number will be 100±y/100 X x

**Example The price of a computer is Rs 20000. What will be the price of computer after reduction of 25%?**

(a)Rs 12000

(b)Rs 18000

(c)Rs 15000

(d)Rs 16000

**Example If A’s income is 50% less than that of B’s, then B’s income is what per cent more than that of A? SSC (10 + 2) 2010**

(a) 125

(b) 100

(c) 75

(d) 50

**Example If income of Ravi is 20% more than that of Ram, then income of Ram is how much per cent less than that of Ravi?**

(a)13 1/3

(b)15 2/3

(c)14 1/3

(d)16 2/3

- When the value of an object is first changed (increased or decreased) by a% and then changed (increased or decreased) by b%, then

Net effect =[±a±b+(±a)(±b)/100]%

Net effect is increased or decreased according to the (+)ve or (-)ve sign, respectively.

**Example A’s salary is increased by 10% and then decreased by 10%. The change in salary is SSC (10 + 2) 2012**

(a) 0%

(b) 1% decrease.

(c) 1%.increase

(d) 2% decrease

- If the price of a commodity increases or decreases by a%, then the decrease or increase in consumption so as not to increase or decrease the expenditure is equal to [a/100±a] X 100%

**Example If the price of a commodity be raised by 40%, by how much per cent must a householder reduce his consumption of that commodity, so as not to increase his expenditure?**

(a) 23 4/7

(b) 37 4/7

(c) 28 4/7

(d) 27 4/7

**Example. From 2008 to 2009, the sales of a book decreased by 80%. If the sales in 2010 were the same as in 2008, by what per cent did it increase from 2009 to 2010? SSC (10+2) 2012**

(a) 80

(b) 100

(c) 120

(d) 400

- If the population of town is P and it increases (or decreases) at the rate of R % per annum, then

**Example A shopkeeper marks the prices of his goods 20% higher than the original price. Due to increase in demand, he further increases the price by 10%. How much profit will he get?**

(a) 33%

(b) 32%

(c) 34%

(d) 28%

**Example The population of a town is 352800. If it increases at the rate of 5% per annum, what will be its population 2 yr hence. Also, find the population 2 yr ago.**

(a) 388962, 320000

(b) 388962, 388400

(c) 320060, 388900

(d) 380060, 280000

**Reference Corner**

**1. 27 is 3.6% of ? SSC (10 + 2) 2017**

(a) 750

(b) 75

(c) 1500

(d) 1875

**2.50% of a number when added to 50 is equal to the number. The number is SSC (10 + 2) 2015**

(a) 100

(b) 75

(c) 50

(d) 150

**3. If 8% of x = 4% of y, then 20% of x is SSC (10+2) 2014**

(a) 40% of y

(b) 80% of y

(c) 10% of y

(d) 16% of y

**4. At an election there were two candidates. A candidate got 38% vote and lost by 7200 number of votes. The total number of valid votes were SSC (10 + 2) 2014**

(a) 16200

(b) 30000

(c) 13000

(d) 13800

**5.1% of 1% of 25% of 1000 is SSC (10 + 2) 2014**

(a) 0.025

(b) 0.0025

(c) 0.25

(d) 0.000025

**6.If 120 is 20% of a number, than 120% of that number will be SSC (10 + 2) 2014**

(a) 20

(b) 120

(c) 360

(d) 720

**7.A reduction of 10% in the price of a commodity enables a person to buy 25 kg more for Rs 225. The original price of the commodity per kg was SSC (10 + 2) 2013**

(a) Rs 2.50

(b) Rs 1.50

(c) Rs 2

(d) Rs 1

**8. Successive discounts of 30% and 20% is equivalent to a single, discount of SSC (10 +2) 2013**

(a) 44%

(b) 10%

(c) 50%

(d) 40%

**9. A reduction of 20% in the price of sugar enables Mr. Bhadra to buy an extra 5 kg of it for Rs 320The original rate of sugar is SSC (10+2) 2013**

(a) Rs 12 per kg

(b) Rs 15 per kg

(c) Rs 16 per kg

(d) Rs 20 per kg

**10. Two numbers are respectively 25% and 40% less than a third number. What per cent of the first is the second? SSC (10+2) 2013**

(a) 60

(b) 70

(c) 40

(d) 80

**Practice Exercise**

**1. A batsman scored 110 runs, which included 3 boundaries and 8 sixes. What per cent of his total score did he make by running between the wickets?**

(a) 45

(b) 45 5/11

(c) 54 6/11

(d) 55

**2. A statue of 80 kg contains 60% copper, 15% zinc and remaining aluminium. After melting, if 5% aluminium is removed. Find the quantity of aluminium required to make the statue.**

(a)21 1/19kg

(b)17 5/19kg

(c) 36kg

(d) 44kg

**3. In a town, the population was 8000. In one year, male population increased by 10% and female population increased by 8% but the total increased by 9%. The number of males in the town was**

(a) 4000

(b) 4500

(c) 5000

(d) 6000

**4. In an election between two candidates 75% of the voters cast their votes out of which 2% votes were declared invalid. A candidate got 9261 votes which were 75% of the valid votes. The total number of voters enrolled in that election was**

(a) 16000

(b) 16400

(c) 16800

(d) 18000

**5. In a mixed school 20% of the scholars are infants under 8 and the number of scholars above 8 is 2/3 of the number of scholars of 8 and amounts to 48. Find the number of scholars in the school.**

(a) 72

(b) 120

(c) 80

(d) 150

**6. If 20% of man’s salary is paid as rent, 60% as his living expenses and 10% is paid in L.I.C. If he spends remaining Rs 30 on the education of the children. Find his salary.**

(a)Rs 300

(b)Rs 100/3

(c)Rs 3000

(d)Rs 900

**7. Out of a total population of 5000 people in a village the men increased by 10% and women by 15%, thus the total population becomes 5600 in a year. Find how many men were there in the village?**

(a) 2000

(b) 3000

(c) 4000

(d) 2500

**8. In an examination 70% of candidate passed in English, 80% passed in Mathematics, 10% failed in both subjects. If 144 candidates passed in both, the total number of candidates was**

(a) 125

(b) 200

(c) 240

(d) 375

**9. A man’s working hours, a day were increased 20% and his wages per hour were increased by 15%. By how much per cent were his daily earning increased?**

(a) 38

(b) 35

(c) 5

(d) 40

**10. Price of the sugar rises by 20%. By how much per cent should the consumption of sugar be reduced so that the expenditure does not change?**

(a) 20

(b) 10

(c) 16 2/3

(d) 15

**11. The cost price of goods with a bankrupt is Rs 25500 and if the goods had realised in their full value, his creditors would have received 85 paise in the rupee. But 2/5 of the goods were sold at 17% and the remainder at 22% below their cost price. How many paise in a rupee was received by the creditors?**

(a) 82 paise

(b) 68 paise

(c) 67 paise

(d) 65 paise

**12. A person gave 20% of his income to his elder son, 30% of remaining to the younger son and 10% of the balance he denoted to a trust. He is left with Rs 10080. His income was**

(a) Rs 50000

(b) Rs 40000

(c) Rs 30000

(d) Rs 20000

**13, The air consists of 79.2% of Nitrogen, 20.7% of Oxygen, 0.08% of other light gases and the remaining gas is Argon. Find out the volume of the air consisting 1 m³ meter of Argon.**

(a) 500 cu m

(b) 50 cu m

(c) 5 cu m

(d) 5000 cu m

**14. A carpenter undertakes to supply 20000 tables at Rs 17.25 each. He estimates that if 10% are defective which will be sold at 50%, then the profit will be 15% on his whole outlay. When the tables were supplied, 70% of the tables were found defective. What loss did carpenter incure?**

(a)Rs 7800

(b)Rs 16075

(c)Rs 4666.25

(d)Rs 6075

**Answers**

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