1953 AMC 12 第 43 题

Question

若一件商品的价格上涨率为

p

，为保持收入不变，销量的下降率不得超过

d

。则

d

的值为：

If the price of an article is increased by per cent

p,

then the decrease in per cent of sales must not exceed

d

in order to yield the same income. The value of

d

is:

\dfrac1{1+p}

\dfrac1{1-p}

\dfrac p{1+p}

\dfrac p{p-1}

\dfrac{1-p}{1+p}

分别用因子

1+p

和

1-d

表示新价格与新销量

Represent the new price and number sold by factors

1+p

and

1-d

收入相同要求

(1+p)(1-d)=1

Equal revenue requires

(1+p)(1-d)=1

将百分率写成相对于原来数量的比例，收入相同要求

(1+p)(1-d)=1\text{。}

因此

p-d-pd=0

，所以

d=\frac p{1+p}\text{。}

因此，正确答案是 C。

Writing the percentage rates as fractions of the original quantities, equal income requires

(1+p)(1-d)=1.

Hence

p-d-pd=0,

so

d=\frac p{1+p}.

Thus, the correct answer is C.

其他年份的第 43 题