Question

1.
If price of a book is first decreased by 25% and then
increased by 20%, ihe net change in the price of the book
will be
.​

Answer 1

Answer:

10%

Step-by-step explanation:

Let the price be 20x(can be taken as x, etc also).

When the price is decreased by 25% :

Price=original price - 25% of original price

Price = 20x - (25% × 20x)

New Price = 20x - (25/100 × 20x) = 15x

When the price is increased by 20% :

Price = new price - 20% of new price

Price = 15x + (20% × 15x)

Price = 15x + (20/100 × 15x) = 18x

Net change = (initial - final)/initial × 100%

Net change = (20x - 18x)/20x × 100%

Net change = 2/20 × 100% = 10%

Answer 2

Answer:

Given :-

• If price of a book is first decreased by 25% and then increased by 20%.

To Find :-

• What is the net price of the book.

Solution :-

Let, the price of the book be Rs 100

$\dashrightarrow$ Price of a book is first decreased by 25%,

$\implies \sf 100\: -\: 25$

$\implies \sf\bold{\green{75}}$

Again,

$\dashrightarrow$ Again, it is increased by 20%,

$\implies \sf 75 + 20\% \times 75$

$\implies \sf 75 + \dfrac{\cancel{20}}{\cancel{100}} \times 75$

$\implies \sf 75 + \dfrac{1}{\cancel{5}} \times {\cancel{75}}$

$\implies \sf 75 + 15$

$\implies \sf\bold{\purple{90}}$

Now, we have to find the net change in the price of the book :

$\implies \sf Net\: change =\: 100 - \dfrac{90}{\cancel{100}} \times {\cancel{100}}$

$\implies \sf Net\: change =\: 100 - 90$

$\implies \sf\bold{\red{Net\: change =\: 10\%}}$

$\therefore$ The net change in the price of the book is 10%.