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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, 2019

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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
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Jul 16, 2019

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, 2019

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

x=2.5

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Updated on: Jul 17, 2019

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

Last edited by ccheryn on 17 Jul 2019, 01:43, edited 2 times in total.
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Jul 16, 2019

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 =$ 1.41, remember even if those 17 fruits are rotten, we still have to consider their cost.

Profit per unit = 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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Jul 16, 2019

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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Jul 16, 2019

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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Jul 16, 2019

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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Jul 16, 2019

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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Jul 16, 2019

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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