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# A retailer orders u units of an item for which he pays d dol

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A retailer orders u units of an item for which he pays d dol [#permalink]

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11 Mar 2013, 23:38
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A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Mar 2013, 01:55, edited 1 time in total.
Edited the question.
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Re: A retailer orders u units of an item for which he pays d dol [#permalink]

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12 Mar 2013, 02:01
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Expert's post
emmak wrote:
A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3

Say the retailer ordered u = 4 items for d = 4$(1$ per item). Thus:

He received 4 - 3 = 1 unit for 4$, which is 3$ more than the item actually costs.

Now, plug u = 4 and d = 4 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*4)/4 = 3.

Hope it's clear.
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Re: A retailer orders u units of an item for which he pays d dol [#permalink]

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14 Mar 2013, 01:55
Bunuel wrote:
emmak wrote:
A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3

Say the retailer ordered u = 4 items for d = 4$(1$ per item). Thus:

He received 4 - 3 = 1 unit for 4$, which is 3$ more than the item actually costs.

Now, plug u = 4 and d = 4 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*4)/4 = 3.

Hope it's clear.

Amount per items actually recieved = d/u-3

Amount per items to be recieved = d/u

Overcharged amount = d/u-3 - d/u = 3d/u(u-3)
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Re: A retailer orders u units of an item for which he pays d dol [#permalink]

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14 Mar 2013, 02:07
Expert's post
akshaychandna wrote:
Bunuel wrote:
emmak wrote:
A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3

Say the retailer ordered u = 4 items for d = 4$(1$ per item). Thus:

He received 4 - 3 = 1 unit for 4$, which is 3$ more than the item actually costs.

Now, plug u = 4 and d = 4 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*4)/4 = 3.

Hope it's clear.

Amount per items actually recieved = d/u-3

Amount per items to be recieved = d/u

Overcharged amount = d/u-3 - d/u = 3d/u(u-3)

The retailer received u - 3 items for the price of u items .

The price of u items is d dollars (so, the price of an items d/u dollars);
The price of u - 3 items is d/u*(u -3) dollars;

The difference is d - d/u*(u -3) = (du - du +3d)/u = 3d/u.

Hope it helps.
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Re: A retailer orders u units of an item for which he pays d dol [#permalink]

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14 Mar 2013, 03:17
emmak wrote:
A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3

Algebraic Solution
Amount overcharged = Amount paid by him - Amount he should have paid
Amount he should have paid=
original price of items*total items purchased
$$\frac{d}{u}*(u-3)$$
Amount paid by him was d dollars
Thus amount overcharged = $$d-d*\frac{(u-3)}{u}$$
On solving we get 3d/u
Thus C
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Re: A retailer orders u units of an item for which he pays d dol [#permalink]

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19 Sep 2014, 02:26
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Re: A retailer orders u units of an item for which he pays d dol [#permalink]

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02 Oct 2014, 02:05
Price ............. Quantity ............ Total

$$\frac{d}{u}$$ .................... u .................... d

$$\frac{d}{u}$$ ...................... (u-3) ............... $$d - \frac{3d}{u}$$ (Three pieces less received)

$$Overcharge = d - d + \frac{3d}{u} = \frac{3d}{u}$$

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Re: A retailer orders u units of an item for which he pays d dol   [#permalink] 02 Oct 2014, 02:05
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