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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, 08:32
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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

100 units of fruits cost CP. - $117.5

17% OF 100 = 17 ROTTEN fruits. Remaining fruits are sold able - 83

S.P = 117.5 +90 = 207.5

Unit S.P = 207.5/83 = $ 2.5

Ans - 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 Updated on: 16 Jul 2019, 11:23
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Profit required = 90

Total sale price = 117.5 + 90
= 207.5

since 17 are rotten, only 83 can be sold

Sale price per unit = 207.5/83

= 2.5

Option D

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Originally posted by prashanths on 16 Jul 2019, 08:35.
Last edited by prashanths on 16 Jul 2019, 11:23, edited 1 time 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, 08:38
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Given that: total cost price = $117.5
total in a pack = 100 units
since 17% in a pack gets bad
the good ones sold = 100 - 17 = 83
to get a profit of $90

thus, total revenue = 117.5 + 90 = 207.5
selling price per unit = 207.5/83 = $2.5

Hence answer choice 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, 08:42
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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?


We are given that:
fruits pack has 100 units N = 100
Total Cost C = $117.5
17% of fruits got rotten, thus are not good for eating.
Profit (P) = $90
What is the selling price for 1 unit to earn this profit (p=?)?

First, let us find out how many fruits are good for eating and are not rotten since we cannot sell rotten goods: 100 * (100% - 17%) = 83
We also know, that the profit is $90. Thus, the total Revenue is P (Profit) + C (Cost) = 117.5 + 90 = 207.5
Our goal is to find out the selling price (p), thus the selling price for 1 unit will be the p = Total Revenue / Number of Good Fruits = 207.5 / 83 = $2.5
Thus, the selling price for 1 unit is $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, 08:43
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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?

Fairly simple question. All you have to do is simplify. Out of the 100 units, 17% are rotten which means that the seller can sell only 83 units. Now the seller wants to earn a profit of $ 90. Which means his revenue should be 117.5+90 = 207.5
Price per unit = 207.5 / 83 = 2.5 Answer .

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

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, 08:45
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Total Cost Price (CP) of 100 units = 117.5 $

17% of 100 units are rotten. Hence, 100-17 = 83 units can be sold.

We need to find Selling Price (SP) of 83 units such that the profit earned is 90$.

Let, this SP be 's'.

Total Profits = Total SP - Total CP
ie, 90 = 83s-117.5

Solving we get s = 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, 08:46
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17% of 100 less is 83

So he brought all fruits for 117.5

He must now sell them each at 2.5 because

83*2.5=207.5

So 207.5-117.5=90

90 is the profit needed

D for.me

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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, 08:46
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from the given, we have \(83\) fruits left, and the incurred cost for all the \(100\) units is $\(117.5\),
so the 83 units can be the only source of revenues to achieve at least $\(90\) profit

Revenues - costs ≥ profit
\(83c - 117.5 ≥ 90\)
\(83c ≥ 207.5\)
\(c ≥ 2.5\), so the least value for the selling price is at least $\(2.5\) per unit fruit.
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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, 08:48
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There are 100 units of fruit out of which 17% of the fruits are rotten. That gives us 100-17 = 83 fruits which can be sold.
The cost price of the 100 fruits bought was $117.5
The selling price the seller wants to sell it at is $117.5 + $90 (As profit) = $207.5.
To find the unit selling price we need :

=\(\frac{Selling price}{number of units}\)

= \(\frac{207.5}{83}\) = $2.5

Hence, option 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, 08:48
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


n=100
cost=117.5
qty=100*83%=83
profit=price•qty-cost… 90=px83-117.5…px=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, 08:49
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The grocer has bought 1 pack of 100 units of fruit for $117.5, but 17% or 17 units out of the 100 are rotten and thus can not be sold, therefore, he has in fact paid 117.5 for 100-17=83 units of fruit. Now the question asks us to compute the selling price such that the grocer makes profit of $90. In other words the grocer will have to sell the 83 units of fruit for 117.5 + 90= $207.5 or each unit for \(\frac{207.5}{83}=$2.5/unit\)

Answer is thus D.

Note: a quick way to deal with the awkward division of 207.5 by 83 is to realize that 83*2= 166 and 83*3= 249, it will then be apparent that 249-207.5=41.5 which is obviously half of 83 and the answer is thus 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, 08:50
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out of 100 17 are rotten ==> 83 remaining.

Cost price is 117.5
profit needed = 90

so selling price for all the available(83) units is 117.5+90 = 207.5

price per unit = 207.5/83 = 2.5

Hence, 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, 08:50
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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?

Profit =(Selling price) - (cost price )
Profit =90
Cost price =117.5
.: Selling price=90+117.5=207.5

Total units =100 , Units rotten =17/100•100=17 ,Not rotten=83

Now the least unit to earn a profit of 90 =
(Total selling price) /(not rotten )=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, 08:53
1
17% of 100 fruits are rotten, then 83 units are in good shape. Total Cost $117.5 & $90 profit has to be made selling those 83 items;

now selling price = cost + profit

SP=$117.5+ $90 = $207.5

So, to maintain this profit & sell those 83 fruits total at this cost, minimum per unit price has to be 207.5/83=2.5

Hence option 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, 08:54
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Given that 100 units of fruits cost $117.5

17% i.e. 17 fruits are rotten. Hence, the number of fruits that can be sold are = 83
To make a total profit of $90 while selling, we need to sell 83 units of fruit at $117.5 + $90 = $ 207.5

Therefore, selling price of each is: \(\frac{$207.5}{83}\) = $ 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, 08:56
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83 fruits are good
and
SP=(90+117.50)/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, 08:57
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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?

If a pack has 100 units and 17% are rotten, then 17 fruits are rotten and we can sell 100-17=83 fruits
We need to earn a profit of 90$. Thus our total price for all 83 fruits should be 117.5+90=207.5
To calculate the price for each unit just divide total price on the quantity of units 207.5/83=2.5

IMO 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 Updated on: 16 Jul 2019, 22:42
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\(100\) units cost \($117.5\). \(17\)% or \(17\) units are rotten. We have \(83\) units out of which we want to make a profit of \($90\).

The total revenue we need \(= 117.5+90=207.5\)

The price for each of 83 units \(= \frac{207.5}{83}=2.5\)

Hence D
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Originally posted by JonShukhrat on 16 Jul 2019, 08:58.
Last edited by JonShukhrat on 16 Jul 2019, 22:42, edited 1 time 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, 09:01
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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?

Total Units = 100
Total Cost = 117,5
RottenUnits = 17%
TotalProfit = 90

1. Let's determine the number of units that we will sell:
SellUnit=100*0,83=83

2. Let's calculate the price per unit :
83*p-117,5=90
p=207,5/83
p=2,5

ANSWER D

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 Updated on: 16 Jul 2019, 09:03
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Let's begin from the end
1) We want to gain $90 total profit
We have 117.5 cost
We want 117.5+90=207.5 total revenue

2) We have to assume that we cant cheat and sell rotten fruit :)
17% is rotten out of 100
We are left with 100-17=83 sellable fruit

3) To earn 207.5 total revenue with 83 fruit
we have to sell each 207.5/83=2.5

IMO
Ans: D

Originally posted by LevanKhukhunashvili on 16 Jul 2019, 09:02.
Last edited by LevanKhukhunashvili on 16 Jul 2019, 09:03, edited 1 time in total.
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