A trader has 60 kg of rice, a part of which he sells at 16% profit and

Question

A trader has 60 kg of rice, a part of which he sells at 16% profit and the rest at 8% loss. On the whole loss is 6%. What is the quantity sold at 16% profit ?

(A) 5 kg
(B) 7 kg
(C) 8 kg
(D) 9 kg
(E) 15 kg

GMATWhizTeam · Accepted Answer

Using the alligation diagram is a very efficient method of solving this question, since the overall loss of 6% is essentially a weighted average of the 16% profit and the 8% loss.
Since the net transaction is a loss, it is not hard to estimate that the part that was sold at 16% profit was a relatively small proportion of the total quantity.

Attachment:

13th Apr 2022 - Post 4.png [ 5.02 KiB | Viewed 9754 times ]

Note that we have considered the loss values as positive here, therefore the profit value is appearing as negative on the diagram.

From the bottom half of the diagram, it is clear that the ratio in which the total quantity of 60kg is to be divided is 11:1, the 1 representing the part that was sold at 16% profit.

Therefore, quantity sold at 16% profit = \(\frac{1 }{ 12}\) * 60 = 5kg.

The correct answer option is A.

rajatchopra1994 · Answer

Explanation:

Let quantity sold at 16% is x

1.16x + 0.92(60-x) = 0.94*60
1.16x - 0.92x + 60*0.92 = 0.94*60
0.24x = 60(0.94-0.92)
x = 60*0.02/0.24
x = 5 kg

IMO-A

Posted from my mobile device

satishov · Answer

This can be done using weighted averages.

We know from question stem that net loss is 6%

So there are two types transactions that have happened 
1. Sell at 16% profit 
2. Sell at 8% loss

If we can get ratio of these transactions then we can get weight of rice sold at 16%

(Xmax - Xmean)/(Xmean - Xmin)

Loss is taken is negative percentage

|(16 - (-6))|/|((-8)-(-6))|=22/2

=11/1

That rice sold at 8% loss is 11 times rice sold at 16% profit.

It can be deduced as 5 kg of rice is sold at 16% profit

Here, it's important to note in weighted average, numerator and denominator cannot be negative. As we are talking of distances from mean position or mean value..

Hope it helps.

Posted from my mobile device

lucasd14 · Answer

Using Alligation, we get that the ratio is 2:22 or 1:11 = 16:(-8). Therefore, the 16% profit is 60 * 1/12 = 5kg.

landwe12321 · Answer

X = Profit
Y = Loss

X + Y = 60, or Y = 60 - X (since we are solving for X)

16x - 8y = -360

16x - 8(60 - x) = -360

16x - 480 + 8X = -360

24x = 120

x = 5

Answer: A, 5kg

ashishpathak · Answer

kindly see if this approach is correct,
from profit is 16% and loss is -8%. imagine on a number line +16 to -8.
we have 24 units between these limits.
also, the final profit/loss is -6 % closer to -8 percent we can safely say that more amount of rice was sold at 8% loss than 16% profit.
If we have 24 units and the final figure is 2 units away from -8. Each percentage point of profit/loss is 60/24=2.5
and two units will be equal to 2.5X2=5 kgs 
so 5 kg of rice was sold at 16 % profit.

azamatboden · Answer

/ 60 = -6 using weighted averages

ScottTargetTestPrep · Answer

Let the cost of one kilogram of rice be c, let the amount sold at 16% profit be x kg.

The x kg of rice were sold at 16% profit, which means the selling price was 1.16c per kg. Thus, the revenue from this part was x * 1.16c.

The rest of the rice, which is 60 - x kg, was sold at 8% loss, which means the selling price was 0.92c per kg. Thus, the revenue from this part was (60 - x) * 0.92c.

In total, the trader earned a revenue of x * 1.16c + (60 - x) * 0.92c.

Since the trader bought 60 kg of rice and paid c per kg, the total cost is 60c. We are told that the trader suffered a loss of 6% in total, which means the trader earned 60c * 0.94 in total. Let's set this amount equal to the expression we obtained earlier:

\Rightarrow  x * 1.16c + (60 - x) * 0.92c = 60c * 0.94

\Rightarrow  c(x * 1.16 + (60 - x) * 0.92) = 60c * 0.94

\Rightarrow  1.16x + 60 * 0.92 - 0.92x = 0.94 * 60

\Rightarrow  1.16x - 0.92x = 0.94 * 60 - 0.92 * 60

\Rightarrow  0.24x = 0.02 * 60

\Rightarrow  24x = 2 * 60

\Rightarrow  x = 120/24 = 5

We see that 5 kilograms of rice were sold at 16% profit.

Answer: A

DonBosco7 · Answer

given total quantity = 60 kg

let x kg sold  Profit  16%
let (60-x) kg sold  loss  8%
overall 60kg sold  loss  6%

remember profit = (+) & loss = (-)

hence => 16% x - 8% (60-x) = -6% (60)

solving this gives => x = 5kg

soniasw16 · Answer

Can an expert clarify if this method is ok?

luisdicampo · Answer

Deconstructing the Question

Total rice =  60 kg .

Part sold at  +16% .
Remaining sold at  -8% .

Overall result =  -6% .

Use alligation (weighted average shortcut).

Step-by-step

Distance from +16% to -6%:

16 - (-6) = 22

Distance from -8% to -6%:

-6 - (-8) = 2

Ratio of quantities:

2 : 22 = 1 : 11

Total parts:

1 + 11 = 12

Each part:

\frac{60}{12} = 5

Quantity sold at +16%:

1 	imes 5 = 5

Answer: A

A trader has 60 kg of rice, a part of which he sells at 16% profit and

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A trader has 60 kg of rice, a part of which he sells at 16% profit and

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