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A pack of fruits has 100 units and its total cost is $117.5. If 17% of

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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 11:11
1
Given,

Total units in a pack of fruits = 100
Total cost of a pack of fruits = 117.5$
Total profit to be earned = 90$
Number of rotten fruits in a given pack = 17

To find,
Minimum selling price per unit of fruit in a pack of fruits to get a profit of 90$

Assumption = Rotten fruits do not get sold.

Let unit selling price of each non rotten fruit be x

Number of non rotten fruits * Selling price of each non rotten fruit = Total cost price + Total target profit
=>
x * (100 - 17) = 117.5 + 90
83 * x = 207.5
x = 2.5

Answer: D
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 12:03
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"A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?"

We know that 17% of 100 fruits are rotten, so we will be able to sell only 83 fruits.
Let X be the selling price which will bring us a total profit of $90.

The equation will be:

83*x = 117,5 +90
83*x = 207,5
x=2.5

So the unit selling price should be $2.5 to earn us a total profit of $90.

The answer is D
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 12:16
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Answer is D

A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

1. 17% of fruits in a pack are rotten => # of "sellable" fruits \(= (1-0.17)*100 = 83\).
2. Cost of all fruits: 117.5
3. Set up equation to find out price that equal or more than $90: [PRICE*# of sellable fruits - cost of all fruits >= 90] => \([X*83 - 117.5>= 90] => [x>=(90+117.5)/83]=>[x>=2.5]\)
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New post 16 Jul 2019, 12:37
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

100 fruits for 117.5 $.
17% fruits are rotten so out of 100, 17 are rotten and 83 are good.
We need a profit of 90.
So total selling price of 83 fruits will be 117.5 + 90 = 207.5

Unit selling price = 207.5 / 90 = 2.5

Answer: D

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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 13:03
1
the total cost of 100 unit = 117.5

rotten (17% of 100 unit) = 17
avialable unit for sale = 100-17 = 83

we need to get a total profit of 90
profit = selling price - cost price
90 = SP - 117.5
SP = 207.5

this is SP of 83 units

let x be the SP of 1 unit then
SP of 83 units = 83x = 207.5
83x = 207.5
x = \(\frac{207.5}{83}\) = 2.5 (unit SP to earn a total profit of 90)

D is the answer
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 13:54
1
Total fruits in a pack =100 at a total cost of $117.5.
We have been informed that 17% is rotten. Therefore units of fruits left for sale = 83

We need to make a profit of $90 from the sale of 83 units, how much do we have to at least sell each unit of fruit to achieve the projected profit.

To attain $90 profit we need to sell the remaining units at a total price of $90+$117.5 =$207.5
Cost per unit is therefore 207.5/83 =$2.5.

The answer is therefore D.

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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 15:23
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Total cost - 117.5$
Profit we need - 90$
Selling price = 207.5$

17% fruit got rotten from the unit of 100.

So left 83 unit .

Selling price of each unit = 207.5$/83 = 2.5 $

Ans - D
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 16:07
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out of 100 . 17% are rotten
therefore items left= 83

also costprice=117.5
profit=90
selling price=117.5+90=207.5

unit price=207.5/83=2.5
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 17:22
1
Profit = SP-CP
CP=117.5
SP for 83 fruits since 17% are rotten ;
profit=90$
90=83*x-117.5
solve for x ; 2.5$
IMO D


A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

A. $2.2
B. $2.3
C. $2.4
D. $2.5
E. $2.6
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 17:41
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Target Revenue = Total Cost + Target Profit = \($117.5 + $90 = $207.5\)

Maximum units of fruits to be sold = \((1-0.17) * 100\) units \(= 83\) units

The minimum unit selling price to earn $90 profit = \(\frac{{Target Revenue}}{{max. unit}}\) = \(\frac{{$207.5}}{83}\) = \($2.5\)

Thus, the minimum unit selling price to earn the target profit is \($2.5\) \(-\) Answer is (D)
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 19:51
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

Given : 100 Units in 1 pack , Of which 17% are rotten = 83Units in a pack are good

Buying Cost = 117.5
Profit expected = 90
===> Selling Cost = 117.5+90
= 207.5 dollars
Units remaining = 83
===> 83 units should be sold for 207.5 dollar
===> Selling cost per unit = 207.5/83
= 2.5 Dollar ---Option D
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 21:57
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

Selling price = 117.5 + 90 = $207.5

Units of fruits which can be sold (not rotten) = 83 units.

So, selling price of each fruit = 207.5/83 = $2.5


ANSWER: D
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 22:07
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

A. $2.2
B. $2.3
C. $2.4
D. $2.5
E. $2.6

Correct answer D

Out of 100 units, if 17% are rotten, then there are only 83 units remaining that could be sold.

On a cost of $117.5, to make a profit of $90, the total revenue from the sale of 83 units should be atleast 117.5 + 90 = 207.5.

83 * X >= 207.5, where X is the selling price of each unit
Hence, X >= 207.5/83 --> X >= 2.5

(Since division of 207.5/83 is not straight forward, at this point you could also use back solving by trying to pick the numbers from answer choices and multiplying with 83 to check if the total is greater than or equal to 207.5. Starting with D helps because 2.5 is easier to multiply with 83)
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 22:20
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CP - 117.5$
Profit - 90$
So, SP = CP+ Profit = 117.5+90 = 207.5

No of fruits to be sold = 83
SP of one unit = 207.5/83 = 2.5

D is correct.
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 22:51
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Percentage of fruits rotten = 17%
Suppose the pack had 100 fruits out of which seventeen are rotten.
So Good fruits - 83
To earn a profit of 90 the total selling price should be 117.5 + 90 = 207.5
Per fruit selling price will be then - 207.5 /83 = 2.5
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 23:01
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

A. $2.2
B. $2.3
C. $2.4
D. $2.5
E. $2.6

17% of 100 is 17. Number of units of non-rotten fruits is 83=100-17. Seller purchased all of fruits for 117.5$ and wants to earn 90$. So he must sell for 207.5$ 83 units. Price per unit is 207.5/83=2.5 D
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 23:17
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

A. $2.2
B. $2.3
C. $2.4
D. $2.5
E. $2.6

Sol:
As 17% are rotten, we have 83 fruits that have to be sold.
CP = $117.5 and we want the SP to be at least $117.5 + 90 = $207.5
So, SP for each fruit = 207.5/90 = 2.5

The answer is (D).
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 16 Jul 2019, 23:28
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?

A. $2.2
B. $2.3
C. $2.4
D. $2.5
E. $2.6

Given: 100 units fruits out of which 17% rotten . so we have 83 units of fruits that cost us- $117.5 so cost per unit =117.5/83
We want to make profit of $ 90

Per unit we need to charge 117.5 + 90/ 83=$ 2.5

Ans choice D
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 17 Jul 2019, 00:09
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A pack of fruits has 100 units and its total cost is $117.5. If 17% of fruits in a pack are rotten, at least what is the unit selling price to earn a total profit of $90?


100 fruit units = $117.5
17% of the fruits are rotten, so 83 fruit units can be sold to make some profit.

We need to make +$90 profit to our total cost, even if 17% of fruit unites are rotten we still need out money back.

So $117.5 + $90 = $207.5
We will divide this number to the number of fruit units that can be sold - 83

$207.5 / 83 = $2.5


A. $2.2
B. $2.3
C. $2.4

D. $2.5
E. $2.6


D is the answer. :heart
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of  [#permalink]

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New post 17 Jul 2019, 00:14
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No. of fruits which can slod from the pack=100-17=83
Total revenue expected= Cost+Profit =117.5+90=207.5

Unit Selling Price= \(\frac{207.5}{83}\)= $2.5

Ans. D
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of   [#permalink] 17 Jul 2019, 00:14

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