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16 Jul 2019, 07:00
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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

### Show Tags

16 Jul 2019, 07:07
2
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

### Show Tags

16 Jul 2019, 07:05
3
Let SP of single fruit be x
83x-117.5=90

x=2.5

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Manager
Joined: 15 Jun 2019
Posts: 151
A pack of fruits has 100 units and its total cost is $117.5. If 17% of [#permalink] ### Show Tags Updated on: 17 Jul 2019, 01:43 1 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 : total units, and total cost price which is 117.5 dollars. out of which 17% are rotten so 17% of 100 which is 17 rotten so now number of fruits remaining is 100 - 17 = 83. total profit is$90

so total selling price = cost price + profit
117.5 + 90 = 207.5 dollars

so net minimum selling price ie one has to price the remaining units to the total selling price = total selling price / no of units left.

= 207.5/ 83

= 2.5 dollars

ie ans D

Originally posted by ccheryn on 16 Jul 2019, 08:05.
Last edited by ccheryn on 17 Jul 2019, 01:43, edited 2 times in total.
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of [#permalink] ### Show Tags 16 Jul 2019, 08:12 1 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

Solution:

We need to find the selling price per unit of the fruit.

Selling Price - Cost Price = Profit,
Therefore Cost per unit + Profit Per unit = Selling price per unit.

Cost price per unit can be obtained by dividing the total cost by the number of units. i.e $$\frac{117.5}{83}$$=$1.41, remember even if those 17 fruits are rotten, we still have to consider their cost. Profit per unit = $$\frac{90}{83}$$ units =$1.09 Per unit.

Therefore, Selling price per unit will be $1.41 +$1.09 = $2.5 Hence the answer is D _________________ Manager Joined: 24 Jun 2019 Posts: 66 Re: A pack of fruits has 100 units and its total cost is$117.5. If 17% of  [#permalink]

### Show Tags

16 Jul 2019, 08:14
1
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?

Total units = 100
% of Rotten Units = 17%
Number of Rotten Units = 17
Remaining Good Units that can be sold = 83

Expected profit = 90$Cost = 117.5$
Minimum Total Selling Price = 90+117.5 = 207.5$Minimum per unit selling price to get 90$ profit = 207.5/83

We could dicide to get the answer, BUT, MANUAL DIVISION IS DIFFICULT

In my opinion it will be easier to multiply the answer choices with 83 to see if we get 207.5

A - 2.2
83x2.2 = 182.6.... Discarded... It will not give 90$profit A was 2 far, so lets skip B and try C (we can always come back to B) C - 2.4 83x2.4 = 199.2.... Discarded... It will not give 90$ profit

D - 2.5
83x2.5 = 207.5
.... Bingo! This is the least sellping price that will give exactly 90$profit Answer - D - 2.5 DS Forum Moderator Joined: 19 Oct 2018 Posts: 1853 Location: India A pack of fruits has 100 units and its total cost is$117.5. If 17% of  [#permalink]

### Show Tags

16 Jul 2019, 08:50
1
Cost price of 100 units of fruits= $117.5 Number of units that are available to sell= 100-(17% of 100)=83 Least Selling price of the 83 units in order to earn$90 profit= 117.5+90=$207.5 Least selling price per unit= Total selling Price/Available units to sell= 207.5/83=$2.5
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Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of [#permalink] ### Show Tags 16 Jul 2019, 10:11 1 Given, Total units in a pack of fruits = 100 Total cost of a pack of fruits = 117.5$
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

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Location: United States
Re: A pack of fruits has 100 units and its total cost is $117.5. If 17% of [#permalink] ### Show Tags 16 Jul 2019, 21:07 1 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

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] ### Show Tags 16 Jul 2019, 23:09 1 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. _________________ My SC approach flowchart My Verbal Flashcards (no one is ideal, please correct if you see any mistakes or gaps in my explanation, it will be helpful for both of us, thank you) ___________________ "Nothing in this life is to be feared, it is only to be understood" ~ Marie Curie Re: A pack of fruits has 100 units and its total cost is$117.5. If 17% of   [#permalink] 16 Jul 2019, 23:09