Apple (A) = 40 cemts
Orange (B) = 60 cents
Average of 10 fruits = 56 cents
u.e. Total Price of 10 Fruits = 56*10 = 560 cents

i.e. 40A + 60 B = 560
and A + B = 10

i.e. 40A + 60 (10-A) = 560
i.e. -20A + 600 = 560
i.e. A = 2
i.e. B = 8

Average to be brought at = 52 cents
let oranges to be put back = C
i.e. Total Fruits = 10-C
where total Oranges left = 8-C
i.e. Total Price of New lot of fruits = 52*(10-C)

i.e. 40*2 + 60*(8-C) = 52*(10-C)
i.e. 80 + 480 - 60C = 520 - 52C
i.e. 8 C = 40
i.e. C = 5

Answer: Option E
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Ans E

Sum of Apples and Oranges is 10

A + O = 10

Apple cost 40 cent and Orange cost 60 cent and there mean is 56 , therefore

(40*A + 60*O)/10 = 56 , which gives us

4A + 6O = 56

Solving the above 2 equation we get , Apples = 2 , Oranges = 8.

Now as she has remove some oranges ( x ) such that the new mean of the remaining fruits become 52

note that the number of Apples remain the same , therefore new equation will become

( 2*40 + (8-x)60 ) / 10 -x = 52

As the remaining fruits will be 10 - x

On solving for x we will get our ans 5

Step 1: We start with the first average to find the total price of the apples and oranges.

Using the formula : Sum = Average * Number of terms
Sum = 56 * 10 = 560

Step 2: Set up the new average based on the first one.
x : number of oranges we need to take away.
We will have the previous sum (i.e. 560) minus the price of all oranges we will take away (i.e. 60x) and the number of elements will be 10 minus x.

So :
(560-60x) / (10-x) = 52
560 - 60x = (10-x) * 52
560 - 520 = -52x + 60x
40 = 8x
x=5

The answer is E.

Hi!

I used the exact same way as you did in solving this question, but when reaching the last part 2:3 I interpereted it as 3/5 oranges and 2/5 apples? Seeing as we're still closer to 60 than 40. And then we should have 6 oranges and 4 apples? Please explain!

Solution:

We can let the number of apples = x and the number of oranges = y. Using these variables we can create the following two equations:

1) x + y = 10

Using the formula average = sum/quantity, we have:

2) (40x + 60y)/10 = 56

Let’s first simplify equation 2:

40x + 60y = 560

4x + 6y = 56

2x + 3y = 28

Isolating for y in equation one gives us: y = 10 – x.

Since y = 10 – x, we can substitute 10 – x for y in the equation 2x + 3y = 28. This gives us:

2x + 3(10 – x) = 28

2x + 30 – 3x = 28

-x = -2

x = 2

Since x + y = 10, then y = 8.

We thus know that Mary originally selected 2 apples and 8 oranges.

We must determine the number of oranges that Mary must put back so that the average price of the pieces of fruit that she keeps is 52¢. We can let n = the number of oranges Mary must put back.

Let’s use a weighted average equation to determine the value of n.

[40(2) + 60(8-n)]/(10 – n) = 52

(80 + 480 - 60n)/(10 – n) = 52

560 – 60n = 520 – 52n

40 = 8n

5 = n

Thus, Mary must put back 5 oranges so that the average cost of the fruit she has kept would be 52 cents.

Answer: E
_________________

A = number of apples
B = number of oranges

We have :

\(\frac{40A + 60 B}{10}\) = 56


and \(\frac{40A + 60 (B - x)}{10 - x}\) = 52

\(\frac{40A + 60 B - 60 x}{10 - x}\) = 52

\(\frac{560 - 60 x}{10 - x}\) = 52

560 - 60 x = 520 - 52 x

40 = 8 x

x = 5

i did this one with a scale method

Apples : Price : Oranges
40 cents : 56 average : 60 cents
= 16 cents from average : average : 4 cents from average
= 1 apple for every 4 oranges
= 2 apples and 8 oranges = 10 fruits = 2*.4 + 8*.6 = 5.60 / 10 = .56

40 cents : 52 average : 60 cents
= 12 cents from average : average : 8 cents from average
= 2 apples for every 3 oranges

8 oranges - 3 oranges = 5 oranges must be put back

Hope this helps!

total amount = avg * number of items
old amount = 56 * 10 = 560

new amount will be 52 *10-x
10-x , you have same number of apples , only decrease in number of oranges
now new amount is equal to what
560 - 60 x = new amount
solve and x= 5

\(\frac{Wa}{Wo} = \frac{(60-56)}{(56-40}) = \frac{1}{4}\)
Apple = 2 & Orange = 8
New Avg
\(\frac{Wa}{Wo} = \frac{(60-52)}{(52-40)} = \frac{2}{3}\)
\(\frac{2}{Wo} = \frac{2}{3}\)
Orange = 3

Hence, Oranges have to reduce from 8 to 3 i.e. 5
_________________

If you analyze enough data, you can predict the future.....its calculating probability, nothing more!

Please find the solution as attached.

Answer: option E

I hope this helps!!!

_________________

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Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
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