Problem Solving

A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?

1:4
1:5
2:3
1:2
2:5

Correct Answer A

rajatvmittal wrote:A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?

1:4
1:5
2:3
1:2
2:5

Correct Answer A

Let C = the cost of each mango, H = the higher selling price, and L = the lower selling price.

Since the mangos are purchased at 5 per dollar, C = 1/5 of a dollar.
Since the higher selling price is 3 per dollar, H = 1/3 of a dollar.
Since the lower selling price is 6 per dollar, L = 1/6 of a dollar.

To break even when the mangos are sold, the average revenue per mango must be equal to C = 1/5 of a dollar.
This is a MIXTURE problem.
A selling price of 1/3 of a dollar (H) is MIXED with a selling price of 1/6 of a dollar (L) to yield an AVERAGE revenue of 1/5 of a dollar (C).
Use ALLIGATION -- a great way to handle mixture problems.

Step 1: Put the fractions over a COMMON DENOMINATOR.
C = 1/5 = 6/30.
H = 1/3 = 10/30.
L = 1/6 = 5/30.

Step 2: Plot the 3 NUMERATORS on a number line, with the numerators for the selling prices (10 and 5) on the ends and numerator for the average revenue (6) in the middle.
H 10-----------6-----------5 S

Step 3: Calculate the distances between the numerators.
H 10-----4-----6-----1-----5 S

Step 4: Determine the ratio of H to L in the mixture.
The required ratio of H to L is equal to the RECIPROCAL of the distances in red.
H:L = 1:4.

The correct answer is A.

For two other problems that I solved with alligation, check here:

https://www.beatthegmat.com/ratios-fract ... tml#484583

Rate of buyig=1/5

Rate of selling in loss=1/6
Rate of selling in Profit= 1/3

loss of one mango=1/5-1/6= 1/30

profit on one mango= 1/3-1/5= 2/15=4/30

So to break even (means Loss= Profit) ratio of the mangoes must be in ratio of the profit and loss=
1/30:4/30=1:4

I am getting the answer 1:2 by applying the weighted average. Dear experts can you please let me know what is the flaw in this approach.

Thank you

Hi,

I used the weighted average approach as well and got 1:2. Not sure why this is wrong.

Here's my solution:

Let the number of mangoes= M. Therefore the total cost is 5M.

The number of mangoes (M) are distributed into two stacks: Say A and B. (M= A+B)

A is sold for $3 and B is sold for $6. Therefore total sales = 3A+6B

From this, we've got two equations:
1) Break-even equation--- 5M = 3A+6B
2) Initial equation---- M = A+B

Solving the two equations we get: A= M/3 and B= 2M/3... Hence, A:B= 1:2

Experts, kindly correct my approach. (I'd appreciate a quick response as my exam's quite close!)

Thanks

Right after my post, I realized my silly error. I read the question wrong!

Corrected solution:

Let the total number of mangoes= M.
5 mangoes---> $1 (20 cents per mango)

Let the two stacks be A and B.
For A: 3 mangoes---> $1 (100/3 cents per mango)
For B: 6 mangoes---> $1 (100/6 cents per mango)

From here on it's the same as my previous solution...
The two equations are:-
1) M= A+B
2) 20M= (100/3)A + (100/6)B

Solving this equation we get A:B = 1:4.

Cheers

Dear experts,
I still am confused with the different solutions provided.
I am getting the answer 1:2 simply by using the alligation method. Also, if we take an example, say I have 30 mangoes.
The total cost price of the mangoes= 5X30= $150
If I sell the mangoes at a ratio of 1:2, the net S.P will be= 10 X 3 + 20 X 6 = 30 + 120 = $150
Thus, it can be seen that using these ratios, the store is having a breakeven as total CP= total SP
Please tell me where I am wrong.

I realized my mistake quickly after submitting the reply.
I was doing a major blunder. The question said 5 mangoes for $1 and not 1 mango for $5. Same for Selling prices also.