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A pack of fruits has 100 units and its total cost is $117.5. If 17% of : Problem Solving (PS)

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Difficulty: 600-700 Level   Word Problems   Source: Math Revolution   

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Jul 16 at 08:00am

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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

 

This question was provided by Math Revolution
for the Game of Timers Competition

 


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Most Helpful Community Reply

Jul 16 at 08:07am

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% percent fruits are rotten.
Hence total number of good fruits = 83
We need to earn a profit of $90. Hence total selling price should be $117.5 + $90 = $207.5
Total fruits to be sold = 83
Hence selling price of each fruit = $207.5/83 = $2.5

Hence Answer = D
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General Discussion

Jul 16 at 08:05am

Let SP of single fruit be x
83x-117.5=90

x=2.5

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Kudos
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Jul 16 at 08:09am

IMO Answer is D:

cost price of 100 units = 117.5$
17 are rotten so, 83 are good to sell
given profit is 90$
So, SP-CP = 90
selling price = 83*x$
83x-117.5 = 207.5 ==> x =2.5$

so answer is D
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Jul 16 at 08:11am

Let the minimum selling price per piece be x,

Then
83*x - 117.5 = 90
x = 2.5
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Jul 16 at 08:14am

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

Cost price of 100 units =$117.5
17% (17 units) are rotten
Saleable units = 100 - 17 = 83
Sales for 83 units = $117.5 + $90 = $207.5
Sales price / unit = $207.5/83 = $2.5


IMO D
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Jul 16 at 08:15am

I went with D:

The total unit cost was $117.5
You need a profit of $90

So revenues need to be at least $207.5
(cost + profit) = Rev. or $117.5 + $90 = $207.5

Since 17% is rotten, you have to earn the revenues through the remaining inventory.
So 207.5/83 = 2.5 per unit
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Jul 16 at 08:18am

SP-CP = 90

CP of fruits = 117.5
SP = 90 + 117.5
SP = 207.5
Since 17% was rotten

SP per unit = 207.5/83 = 25$

Answer should be D
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Jul 16 at 08:23am

100 fruits were bought at $1.175 per fruit ------------------- (Cost Price)

(100-17) fruits are to be sold at $x per fruit, where is x is the average selling price per unit ----------------- (Selling Price)

We require that,
(100-17)x = 100(1.175) + 90

83x = 207.5

x=2.5

Answer is (D)
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Jul 16 at 08:25am

100 units for 117.5$

17% of 100 fruits are rotten. So 83 fruits are not rotten.

For total profit of 90$, sale price should be 117.5+90=207.5

SP of per unit=\(\frac{207.5}{83}\)=$2.5

Hence option D
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Jul 16 at 08:25am

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


SOL:

the total number of fruits=100,
rotten=17
so left=83.

now the CP of 100 fruits=117.5 and we need 90 profit.
so we must sell 83 fruits for 207.5

that means each fruit has to be at least=207.5/83=2.5

D 2.5 atleast.
Kudos
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Jul 16 at 08:27am

The total fruits we have is 83 and profit is $90, so the total selling cost would be 117.5+90=207.5.

So unit selling price = 207.5/83=2.5

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Kudos
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Jul 16 at 08:27am

D

The packet has total 100 units of fruits and 17% or 17 units are rotten. That means that only 83 fruits have any worth.

Now, the cost of the packet is $117.5, however, we need $90 profit margin.

So, the packet should be selling for $117.5+$90 = $207.5

The packet has 83 units, so each unit should sell for 207.5/83 = $2.5/unit
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Jul 16 at 08:28am

IMO- D

Total Units = 100 units
Total cost = $117.5

Fruits rotten/park= 17% = 0.17 X 100= 17 Units
Fruits Ok = 100-17= 83 units
Total profit = $90

Total SP for 83 Units= $117.5 + $90 = $207.5
Least SP/Unit= $207.5/83 = $2.5

For any SP/unit greater than $2.5 profit will be greater than $90
Ans- D
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Jul 16 at 08:28am

Cost - 117.5 $ and Profit required - 90$. Total sales value - 207.5 and units available - 83. So per unit cost - 207.5/83 (sub answer options in 83*X=207.5)

2.4$ per fruit gives 199.2$. So unit price must be higher. 2.5$ gives 207.5 IMO D
Kudos
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Jul 16 at 08:29am

Selling Price = Total cost + Profit
Total cost=117.5
Profit=90(Minimum)

SP=117.5+90=207.5

Now, as 17% units are rotten, we need to get profit from 83% which is 83 units.

So SP of each unit = 207.5/83=2.5
Hence D
Kudos
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Jul 16 at 08:29am

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?

Profits = Selling Price* #of units - Costs

So, if rotten units are 17%, we will have only 83 units, so

90 = 83*SP - 117.5

207.5 = 83*SP

SP = 2.5

So (D) is our answer.
Kudos
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Jul 16 at 08:29am

Let the selling price per unit be \(x\).

Profit = Total Selling Price (excluding roten units) - Total Cost of the units
\(90 = 83x-117.5\)

Which gives,
\(x=2.5\)
Kudos
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Jul 16 at 08:30am

D has to be the right answer.
90 profit means 117.5 + 90 = 207.5

And 2.5x83(after reducing 17%) is 207.5

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Jul 16 at 08:31am

Answer D :
Simple and straight :
C.P : 117.5
S.P : 117.5 +90 = 207.5
Unit price: 207.5/100 = 2.075
now 17% of fruits are bad, so left fruits: 83 ,
Now to earn 90$ profit, S.P cannot be changed but unit price will increase So
207.5 / 83 = 2.50
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