Question

6. The difference between increasing a number by 5% and decreasing it by 5% is 20.
What is the number?
7. A number is increased by 20% and then it is decreased by 10%. Find the net
increase or decrease per cent.formula and the answer will be 8%​

Answer 1

Question 6:

Given that:

• The difference between increasing a number by 5% and decreasing it by 5% is 20.

To Find:

• What is the number?

Let us assume:

• The certain number be x.

Finding the number:

According to the question.

⟶ x + 5% of x - (x - 5% of x) = 20

⟶ x + 0.05x - x + 0.05x = 20

⟶ 0.1x = 20

⟶ x = 20/0.1

⟶ x = 200

Hence,

• The required number is 200.

Question 7:

Given that:

• A number is increased by 20% and then it is decreased by 10%.

To Find:

• The net increase or decrease percent.

Let us assume:

• The number be 100.

When number is increased by 20%,

• Number = 100 + 20% of 100
• Number = 100 + 20
• Number = 120

When it is decreased by 10%,

• Number = 120 - 10% of 120
• Number = 120 - 12
• Number = 108

We have:

• Final value = 108
• Initial value = 100

When final value is greater than the initial value then it is net increase.

We know that:

• Percentage, % = {(Final value - Initial value) × 100}/(Initial value) %

Finding the percentage:

⟶ Percentage = {(108 - 100) × 100}/(100) %

⟶ Percentage = {8 × 100}/(100) %

⟶ Percentage = 800/100 %

⟶ Percentage = 8 %

Hence,

• The net increase percent is 8%.

Answer 2

6]

Given :-

The difference between increasing a number by 5% and decreasing it by 5% is 20.

To Find :-

Number

Solution :-

Let the number be a

When increased by 5%

x + 5x/100

x + x/20

20x + x/20

21x/20

When decreased by 5%

x - 5x/100

x - x/20

20x - x/20

19x/20

Now

Difference = 20

21x/20 - 19x/20 = 20

21x - 19x/20 = 20

2x/20 = 20

x/10 = 20

x = 10 × 20

x = 200

7]

Given :-

A number is increased by 20% and then it is decreased by 10%.

To Find :-

Net  increase or decrease per cent

Solution :-

Let the number be 100

When increased by 20%

20% of 100

20/100 × 100

20

Now

Increased number = 100 + 20 = 120

When decreased by 10%

10% of 120

10/100 × 120

1/10 × 120

12

Decreased number = 120 - 12 = 108

Now

Increase in % = 108 - 100 = 8%

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