Percentage Problems With Solutions, deals with various concepts which are as under:-

- Finding a number, whose percentage value is given
- Finding what percentage of a given term is another term
- Net Increase or Decrease Percentage in a Number
- Finding a number when its decreased percentage is given
- Finding a number when its increased percentage is given
- Salary saved

**Percentage Problems With Solutions – Finding a number, whose percentage value is given**

**Question 1:**

If 30 % of a number is 60, find the number?

**Solution:**

We can form a linear equation to express the given statement and then arrive at the number

Let the required number be

We are given that

30 % of is 60

or in other words

x = 60

On cross multiplication, we get

=

= 200

Hence, the number is 200

**Percentage Problems With Solutions – Finding what percentage of a given term is another term**

**Question 2:**

What percent of 20 litres is 10 litres ?

**Solution:**

Let a % of 20 litres = 10 litres

Step 1 – Convert the Percentage into Fraction

i.e a % =

Step 2 – Multiply the Fraction with given quantity.

i.e, ( ) litres = ( 10 ) litres

= 10

a =

a = 50

Hence, 10 litres is 50 % of 20 litres

**Question 3:**

What percent of 100 m is 80 m?

**Solution:**

Let a % of 100 m = 80 m

Step 1 – Convert the Percentage into Fraction

i.e a % =

Step 2 – Multiply the Fraction with given quantity.

i.e, ( ) m = ( 80 ) m

= 80

a =

a = 80

Hence, 80 m is 80 % of 100 m

**Question 4:**

What percent of 70 kg is 49 kg?

**Solution:**

Let a % of 70 kg = 49 kg

Step 1 – Convert the Percentage into Fraction

i.e a % =

Step 2 – Multiply the Fraction with given quantity.

i.e, ( ) kg = ( 49 ) kg

= 49

a =

a = 70

Hence, 49 kg is 70 % of 70 kg

**Percentage Problems With Solutions – Net Increase or Decrease Percentage in a Number**

**Question 5:**

A number is increased by 25 % and then decreased by 8 %. The net increase or decrease percentage is?

**Solution:**

We can form a linear equation to express the given statement and then arrive at the number

Let the required number be “a”

Step I:

If the number is increased by 25 % it would be equal to ( Given Number + 25 % of Given Number )

= ( a + )

= ( 1 + ) a

= ( ) a

=

Step II:

If the number at Step 1 is decreased by 8 % it would be equal to ( Increased Number – 8 % of Increased Number )

= ( – x )

= ( – )

= ( ) a

=

=

Net Increase = ( – a )

= ( )

=

Net Increase Percentage = ( x x 100 )

= 15 %

Hence, Net Increase Percentage is = 15 %

**Percentage Problems With Solutions – Finding a number when its decreased percentage is given**

**Question 6:**

A number when decreased by 20% gives 160. The number is?

**Solution:**

Here we take the help of linear equation. First we will form the equation.

Let the number be ‘a’

20 % of ‘a’ = a

Since, the equation is:

a – a = 160

Taking 100 as LCM on LHS

= 160

a = 160

a =

a = 200

Hence, the number is 200

**Percentage Problems With Solutions – Finding a number when its increased percentage is given**

**Question 7:**

A number, when increased by 25% gives 375. The number is?

**Solution:**

The problem can be solved using linear equation.

Let the number be ‘a’

25% of a = a

We are given that, a + a = 375

Taking 100 as LCM on LHS

= 375

a = 375

a =

a = 300

Hence, the number is 300

**Percentage Problems With Solutions – Salary saved**

**Question 8:**

Shruti spends 60 % of her Salary and saves the rest If she saves ₹ 5960 per month.

**Solution:**

Let Shruti’s monthly salary be ₹ a

Expenditure = 60 % of her Salary

Expenditure = 60 % of ₹ a

= x ₹ a

= ₹

Savings = Salary – Expenditure = 100 % – 60 % = 40 %

Savings = ₹ ( a – )

= ₹ ( )

= ₹

Given,

Savings = 5960 = 40 % of a

₹ 5960 = ₹

a = ₹ ( )

a = ₹ 14900

Shruti’s monthly salary is ₹ 14900

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