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**Chapter - 11**

**PERCENTAGE AND ITS APPLICATIONS**

â€˜Per centâ€™ means â€˜out of one hundredâ€™. Symbol % is used to denote per cent

Some examples to convert a per cent into a fraction, ratio or decimal and vice versa.

**6) (i) 50% = **0.50

**(ii) 7% = **0.07

**(iii) 90% = ** = 0.90

**(iv) 1% =** 0.01

** **

**8) (i) 10% of 100 =** 10

**(ii) 20% of 500 =** 100

**(iii) 30% of 1000 =** 300

**9) (i) 5 out of 25 =** 20%

**(ii) Re 1 out of Rs 25 =** 4%

**(iii) 10 out of 50 =** 20%

**Solved examples:**

**(i) If 25% of X= 30 find X**

**Sol. **25% of X is and it is equal to 30

**(ii) If 4.6% of X is 23 find X**

**Sol.** 4.6% of X means and it is given to be equal to 23

So = 23

or X =

**(iii) If 24% of X is 48, then find x**

**Sol.** 24% of X is 48

**Example 2: Vijay deposits Rs 45 per month in the bank. If this amount is 15% of his monthly income, find his monthly income.**

**Solution: **Let his monthly income be Rs X

As per the given statement 15% of X is 45

or x = = 300 RS

**Example 3: Gunpowder contains 75% nitre and 10% sulphur. The rest of the material is charcoal. Find the amount of each of the contents in 9 kg of gunpowder.**

**Solution: **Weight of gunpowder = 9 kg

Contents are â€“ nitre = 75%, Sulphur = 10% charcoal = 100-75-10 = 15%

Nitre in 9 kg = = 6.75 kg.

Sulphur in 9 kg = = 0.90 kg.

Charcoal in 9 kg = = 1.35 kg.

**Example 4: Priya got 87.5% marks in the annual examination. If she got 700 marks, find the total number of marks in the examination.**

**Solution:** Let total marks be X

A per the statement 87.5% of X = 700

So total marks = 800

**Example 5: The value of a machine depreciates by 10% every year. If its present value is Rs 38700, what was its value one year ago.**

**Solution: **Let the value last year be x

If it is decreased by 10% the present value will be

and as per the given statement

or x = = 4300 X 10 = Rs. 43000.

**Example 6: The salary of a person has been increased by 25%. By what per cent should the salary be reduced so that he gets the original salary.**

**Solution:** Let original salary be 100

Salary after an increase of 25% = 100+25=125

To restore the salary back to 100 it should be decreased by Rs 25

The reduction on 125 = Rs 25

The reduction on 100 =

**Example 7: Ankits salary is 25% more than that of Anil. What percent is Anilâ€™s salary less than Ankits?**

**Solution: **Let Anilâ€™s salary be Rs 100

Then Ankit gets 25% more than Anil = 125

Now If Ankitâ€™s salary is Rs 125 Anilâ€™s = 100.

If Ankitâ€™s salary is Rs 100 then Anilâ€™s =

So Anils salary is Rs 80 when Ankitâ€™s is Rs 100

So Anil salary is 20% less than Ankit

**Example 8: Raman loses 20% of his money. After spending 25% of the remaining, he has Rs 480. How much did he originally had?**

**Solution: **Suppose Raman had Rs 100 in the beginning. He lost 20% i.e. Rs. 20

Remainder = Rs 100 â€“ Rs 20 = Rs 80

Out of Rs 80 he spent 25%, which is equal to

Remainder = Rs 80 â€“ Rs 20 = Rs 60

If remainder is Rs 60, he originally had = Rs 100

If remainder is Rs1, he originally had =

If remainder is Rs 480 he originally had =

** **

**Example 9: The price of wheat increases by 10%. By what per cent should a consumer reduce his consumption so that his expenditure of wheat remains the same.**

**Solution: **Let the original consumption of wheat is 100 kg and the price is Rs 100 per kg.

Expenditure originally = Rs 100 x 100

Expenditure now if consumption is X kg @ Rs 110 per kg = x X 110 Rs

But the expenditure remains to be the same

So x X 110 = 100 X 100

Or

So reduction in consumption =

**Example 10: The price of a shirt in Dec 1997 was Rs 250. In Jan. 1998 it was increased by 10% and in Oct 1998 it was reduced by 10%. What in the new price of the shirt.**

**Solution:** Price in Dec 1997 = Rs 250

Price in Jan 1998 =

Price in Oct 1998 = 275 x = Rs 247.50

**Example 11: In an examination a candidate must secure 40% marks to pass. A candidate got 220 marks and failed by 20 marks. What are the maximum marks for the examination.**

**Solution:** Let the maximum marks be x

Marks required to pass =

As per the statement the marks required to pass = 220 +20 = 240 ------- (ii)

So from I and II

**Example 12: When 75% of a number is added to 75, the result is the same number. Find the number.**

**Solution: **Let the number be x

As per the given statement.

75% of X + 75 = x

Or

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