The price of an item was increased by 25\% and then the new price was decreased by 20\%. W… — GRE General Test

The price of an item was increased by $25\%$ and then the new price was decreased by $20\%$ . Which of the following statements must be true regarding the final price of the item relative to its initial price? Select all such statements.

The final price of the item is equal to its initial price.Cevap
The overall net percent change in the price of the item is $0\%$ .Cevap
The ratio of the final price to the initial price is $1$ to $1$ .Cevap
D
The final price of the item is $5\%$ greater than its initial price.
E
The final price of the item is $5\%$ less than its initial price.

Cevap

The statements confirming that the final price equals the initial price, that the overall net percent change is 0%, and that the ratio of the final price to initial price is 1 to 1 are all correct.

Let

P

be the original price. After a

25\%

increase, the price becomes

1.25P

. Decreasing this intermediate price by

20\%

yields

1.25P \times 0.80 = 1.00P

. Because the final price is identical to the initial price, the final price is equal to the initial price, the net percentage change is

0\%

, and the ratio of final to initial price is

1:1

Adım Adım Çözüm

Represent the initial price with a variable

Let the initial price of the item be

P

Using a variable makes tracking successive percent changes straightforward.

Apply the

25\%

increase

Increased price

= P \times (1 + 0.25) = 1.25P

25\%

increase corresponds to multiplying the base by

1.25

Apply the

20\%

decrease to the new base

Final price

= 1.25P \times (1 - 0.20) = 1.25P \times 0.80 = 1.00P

The

20\%

decrease applies to the updated base value of

1.25P

Evaluate each statement based on the final price

1.00P

The final price equals the initial price (

P

), the net percent change is

0\%

, and the ratio of final to initial price is

1:1

All three true statements directly reflect that the final price is equal to the initial price.

Anahtar Kavram

Successive Percentage Changes and Base Shift

Tahmini Süre:45s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

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