A Merchant has 1000 kg of Sugar Part of Which He Sells at 8% Profit GMAT Problem Solving

Question: A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is:

1. 300
2. 400
3. 600
4. 500
5. 700

Correct Answer: C

Solution and Explanation:
Approach Solution 1:
The given condition to a problem solving question states that a merchant has 1000 kgs of sugar part of which he sells at a profit of 8% and the rest of them at 18%. Overall, the merchant gets a 14% profit. 

The problem requires finding the quantity that was sold at 18% profit.

For this, let the quantity of the sugar sold at 18% profit be x.

Further, let the quantity sold at 8% profit be 1000 - x. 

Now in order to evaluate the entire quantity that has been sold at 18% profit, this can be formulated into an equation where the value of x could be found. 

Now, the entire problem could be solved in the following way: 

18x/100 + 8 * (1000 - x) = 18 * 1000/100 
Or it can be stated as - 10x + 8000 = 18000
Or it can further be evaluated as 10x = 6000 
This implies that the value of x is equal to 600- 
x = 6000/100 = 600

Thus, the quantity of sugar that can be sold in 18% profit can be evaluated to be 600kgs.

Approach Solution 2:
The problem statement informs that:
Given:

• A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit.
• He gains 14% on the whole.

Find out:

• The Quantity sold at 18% profit.

The given problem can also be solved by using the method of weighted average. 

Let the quantity of sugar that he sells at 8% profit be W1.

Let part B of the profit at which he sells the sugar at 18% profit be W2. 

It is given that both quantities are sold at 14% profit which is basically the average profit percent for the quantity of sugar sold. 

Therefore, for using the weighted average to calculate the quantity of sugar sold at 18% profit, the following use of formula needs to be done. 

\(\frac{W1}{W2}=\frac{(B-Average)}{(Average-A)}\)

\(=\frac{18-14}{14-8}\)

\(=\frac{W1}{W2}=\frac{2}{3}\)

\(=W2=\frac{3}{5}*1000\)

= W2 = 600 

Hence, the quantity of the sugar sold at 18% profits has been weighted at 600kgs. 

Approach Solution 3:
The problem statement states that:
Given:

• A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit.
• He gains 14% on the whole.

Find out:

• The Quantity sold at 18% profit.

Let the quantity sold at 8% profit be x
And the quantity sold at 18% profit be y.

Therefore as per the given conditions of the question:
=> 108*x/100 + 118*y/100 = (x+y)*114/100
=> 108x + 118y = 114x + 114y
=> 4y = 6x
=> 2y = 3x
=> x/y = 2/3
=> Therefore, x:y = 2:3
Dividing 1000 in a 2:3 ratio we get:
y = 1000*3/5 = 600
Hence, the quantity sold at 18% profit is 600 kgs.

“A merchant has 1000 kg of sugar part of which he sells at 8% profit”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions enable the candidates to evaluate each fact in order to crack numerical problems. GMAT Quant practice papers help the candidates to analyse several sorts of questions that will enable them to improve their mathematical learning.

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