Question: A trader has 400 kg of rice, a part of which he sells at 36% profit and the rest at 24% loss. On the whole he losses 12%. What is the quantity sold at 24% loss?

(a) 80kg
(b) 100kg
(c) 175kg
(d) 320 kg
(e) 400 kg

Correct Answer: (D)

Approach Solution 1 :

Using the cost price of rice as 100 and the assumption that x is a portion of the rice the trader sells at a loss of 24%, the equation signifying an overall loss of 12% is, 136(1−x)+76x = 88

By solving x, we get
x=4/5

Therefore 4/5 of 400 kg =320 kg

Approach Solution 2 :

Out of 400, some produced 36% profit and the remainder 24% loss.
24% loss can be described as -24% profit.
From this, we obtained the first row of numbers, 36 and -24.

The result is once more a loss of 12%, making the profit -12%; this will appear in the second row.
By the rules of alligation, we get -12 > -24.
By subtracting them, we get - 12 - (-24) = -12 + 24 = 12
Note that 36 > -12

By subtracting again, we get 36 - (-12) = 48
This gives the third row which are 12 and 48.
Now the total will be 12 + 48 = 60.
48 have given a loss of 24%
Therefore the calculation will be,
=> [48/(12+48)] ∗ 400 = 320

Approach Solution 3 :

Consider the cost price of rice per kg as 1 rupees.

Let the quantity of rice sold at 24% loss as x kg.

So now, the quantity of rice sold at 36% profit = (400 - x) kg

From the question, we can write that ,

x*(100−24)% + (400-x)*(136/100) = 400*(100−12)%
=> x*(76/100) = (400−x)*(136/100)
= (400)*(88/100)

=> (76x + 400)*(136-136x)
= 400×88

=> 136x−76x = 400(136−88)
=> 60x = 400*48
=> x = (400*48)/60 = 320 kg.

“A trader has 400kg of rice, a part of which he sells at 36%” - is a subject that the GMAT quantitative reasoning section covers. A school needs to be proficient in a variety of qualitative skills to answer the GMAT Problem Solving questions correctly. There are 31 questions in the GMAT Quant section as a whole. The GMAT Quant topics' problem-solving section calls for the resolution of calculative mathematical puzzles.

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