Question

A number is increased by 15 % and then decreased by 25% and the numbers become 22 less than the original number. the original number ?​

Answer 1

Given:

• A number is increased by 15% and then decreased by 25%.
• The numbers become 22 less than the original number.

To Find:

• The original number?

Let us assume:

• The original number be x.

Number is increased by 15%.

= x + 15% of x

= x = 0.15x

= 1.15x

And then decreased by 25%.

= 1.15x - 25% of 1.15x

= 1.15x - (0.25 × 1.15x)

= 1.15x - 0.2875x

= 0.8625x

Finding the original number:

According to the question.

⟶ 0.8625x = x - 22

⟶ 0.8625x - x = - 22

⟶ - 0.1375x = - 22

Cancelling minus.

⟶ 0.1375x = 22

⟶ x = 22/0.1375

⟶ x = 160

Hence,

• The original number is 160.

Answer 2

Given :-

A number is increased by 15% and then decreased by 25%

To Find :-

Original number

Solution :-

Let the number be a

When increased by 15%

a + 15% of a

a + 15/100a

a + 15a/100

100a + 15a/100

115a/100

Now

When decreased by 25%

115a/100 - 25% of 115a/100

115a/100 - 25/100 × 115a/100

115a/100 - 25 × 115a/100 × 100

115a/100 - 2875a/10000

11500a - 2875a/10000

8625a/10000

Now

8625a/10000 = a - 22

8625a/10000 - a = -22

8625a - 10000a/10000 = -22

-1375a/10000 = -22

1375a/10000 = 22

a = 22 × 10000/1375

a = 160