11+ Maths Solved Topic Wise Questions

1. Percentages

Percentages are widely used in our daily lives. For example, discounts in shopping malls, bank interest rates, Scores obtained in an exam, etc. are expressed as percentages. 

A percentage is a number or ratio that can be expressed as a fraction of 100. It is represented by the symbol “%”. 

For example, if John scored 80% marks on his Maths test, it means that he scored 80 marks out of 100. It is written as 80⁄100 in fraction form and 0.80 in decimal form.  

If we have to calculate the percentage of a number, we divide the number by the whole and multiply by 100. Hence, the percentage is a part per hundred. 

1.1 Percentage of an Amount

Percentage of an amount can be calculated by writing the percentage as a fraction or decimal and then multiplying it by the given amount. 

Example: Find 15% of 200.

Solution:

15% of 50 = 15⁄100 x 200   … 15% = 15⁄100

                 = 15 × 200⁄100

                 = 30

1.2 Reverse Percentages

Problems on reverse percentages require working backwards to find the original amount, given a percentage of that amount.

We follow these steps to find reverse percentages: 

• Put the percentage equal to the amount given.
• Find 1% by dividing both sides by the percentage.
• Find the original amount by multiplying by 100.

Example: 12% of an amount is 48. Find the original amount.

Solution:

The original amount is 400. 

1.3 Increasing or Decreasing an amount by a Percentage

The steps to be followed for increasing or decreasing an amount by a percentage:

• Calculate the percentage of the amount given.
• Add/subtract this answer with the original amount to increase/decrease the amount.

Example: 

(a) Increase £180 by 25%. 

(b) Decrease £80 by 25%.

Solution:

1. Calculate 25% of £180 : 25⁄100 × £180 = £45 

   To increase, add £45 to the original value: £180 +  £45 =  £225

2. Calculate 25% of £80 : 25⁄100 × £80 = £20 

   To decrease, subtract £20 from the original value: £80 -  £45 =  £35

1.4 Percentage Change

Percentage change means by what percentage of its original value something has increased or decreased. It is calculated using the below formula:

Example: 

The number of people attending a dance class has increased from 24 to 30. Calculate the percentage change.

Solution:

Calculate the change: 30 - 24 = 6

Apply the percentage change formula: 

Percentage change = Change⁄Original × 100

                                = 6⁄24 × 100

                                = 25%

As the number of people has increased, this is a 25% increase.