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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, 09:03
1
100 units cost $117.5, so for each unit, the cost is $1.175.
As per the question, 17% of units are rotten, so only 83% will be sold.
Let the selling price be x.
So using Profit = Selling Price - Cost Price
=> 90 = 83*x - 117.5
=> 207.5 = 83*x
=> x = 2.5

IMO the answer is D.

Please hit kudos if you like the solution.
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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 Updated on: 17 Jul 2019, 02:43
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
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Originally posted by ccheryn on 16 Jul 2019, 09:05.
Last edited by ccheryn on 17 Jul 2019, 02:43, 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]

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New post 16 Jul 2019, 09:06
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?

Solution:
s: unit selling price
100 * (100-17)% * s - 117.5 = 90
=> s = (90+117.5)/83 = 207.5/83 = 2.5

A. $2.2
B. $2.3
C. $2.4
D. $2.5 --> correct
E. $2.6
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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, 09:12
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
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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, 09:14
Cost Price: 117.5 $
Selling Price: 117.5+90(profit)=207.5$
# units: 100-17: 83
per unit price: 207.5/83 = 2.3$
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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, 09:14
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
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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, 09:26
1
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?

To earn a total profit of $90, the rest of the fruits will have to be sold at $(117.5+90)=$207.5
17% of 100 units = 17 units of fruits are to be deducted, leaving 83 units
So, the selling price of each fruit = $(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, 09:33
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:
Total Cost price + Profit =Total selling Price
$117.5+$90=$ 207.5=Total Selling Price
Now ,
Total units of fruits=100
Rotten=17% of 100=17
Total remaining fruits that would be sold=100-17=83
Hence the selling price per unit of 83 fruits=\(207.5/83\)=$2.5
Hence D is the answer IMO
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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, 09:34
1
Answer is D.

P=R-C
90=(100(1-17%))*X - 117.5
X=2.50
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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, 09:35
1
since 17% are rotten so, Total units to seel is 100-17=83.
Profit is 90$. so SP = CP+ Profit
=>SP=117.5 +90=207.5
so price per unit = 207.5/83=2.5 $
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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, 09:40
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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

The pack contains 100 units, out of which 17% are rotten, which is 17 units (100*\(\frac{17}{100}\)). So, those fruits that were sold are 100-17=87
He purchased all fruits for $117.5 and wants to make at least $90. So his minimal selling price is $117.5+$90=207.5 for all 83 units or $2.5 per unit (\(\frac{207.5}{83}\)). 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, 09:50
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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]

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New post 16 Jul 2019, 10:07
100 units @ $117.5
17% rotten = 17 out of 100 not fine, 83 left.
to get $90 profit, $117.5 + $ 90 = $207.5 should be total price for 83 units.
Per 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, 10:10
1
Quote:
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


Total fruits = 100
as 17 % rotten, rotten fruits = 17

Now CP= 117.5
as expected profit is 90
SP = Profit +CP
= 117.5 +90
= 207.5
Now remaining fruits = 100-17
= 83
therefore \(\frac{207.5}{83}\) = 2.5

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, 10:15
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 Cost = 117.5.
To earn 90$ profit, total selling price should be = 117.5 + 90 = 207.5$

As 17% of the total 100 units are rotten i.e. 17 units. Remaining units are = 100 - 17 = 83.

So the selling price of an unit should be = 207.5/83 = 2.5 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, 10:26
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?

Cost of each unit = $117.5/100 = $1.175.
Since 17% of fruits are rotten, total fruits to be sold = 83.
To maintain the total profit of $90, total selling price of 83 units should be $117.5+$90 = $207.5

Therefore, selling price of each non rotten unit = $207.5/83 = $2.5


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

Answer 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 16 Jul 2019, 10:29
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

As 17% fruits are rotten, then remained fresh fruits =83
Total selling price should be =117.5 + 90 = 207.5
Unit selling price =207.5 / 83 = 2.5
So, the correct answer choice 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, 10:34
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 Fruits = 100
Rotten = 17
Total Sell-able fruits = 83

Total Selling Price=Cost price + Required Profit = 117.5+90 = 207.5

Selling price per Unit = 207.5/83

Division may become complex... but also the answer choices are really close to each other.. approximating will be a problem
Using the middle number 2.4 * 83 =199
The next bigger number = 2.5* 83 = 207.5

Answer 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, 10:34
1
Total no of fruits = 100
Total cost = 117.5
Total no of rotten fruits = 17% of 100 = 17
Total no of good fruits = 83
Profit to earn = 90
Total selling cost = Cost + Profit = 117.5 + 90 = 207.5
Unit selling price \(\frac{207.5}{83}\) = 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, 10:43
1
Total 100 units are at $117.5
17% units are rotten, effectively 83 units will be remaining for selling

Profit to be earned -> $ 90
Effective Selling Price wud be $117.5 + 90 = $ 207.5

83 units to be sold at $207.5 to get a profit of $90
so 1 unit selling price wud be 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] 16 Jul 2019, 10:43

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