Multiple choice

In what ratio should a person mix three kinds of metal costing Rs. 60/kg, Rs. 75/kg and Rs. 100 /kg so that the resultant alloy when sold at Rs. 96/kg results in a gain of 20%?

  1. 1 : 2 : 4

  2. 3 : 7 : 6

  3. 1 : 4 : 2

  4. 1 : 4 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Selling price = 96, gain = 20%. Cost price = 96 / 1.2 = 80. Using the mixture rule for three components: (60x + 75y + 100z) / (x+y+z) = 80. 60x + 75y + 100z = 80x + 80y + 80z => 20z = 20x + 5y => 4z = 4x + y. Testing options: 1:4:2 gives 4(2) = 4(1) + 4 => 8 = 8. Correct.

AI explanation

The selling price for a 20% gain is Rs. 96, so using the formula Selling Price equals Cost Price multiplied by 1.2, the target cost price of the mixture is 96 divided by 1.2, which equals Rs. 80. Mixing Rs. 60 and Rs. 75 metals gives a deficit of 20 and a surplus of 5 compared to Rs. 80, meaning they must be mixed in a 1 to 4 ratio. Introducing the Rs. 100 metal, the 5 parts of the Rs. 60 and Rs. 75 mixture average to Rs. 80, so adding Rs. 100 creates a new average where the Rs. 100 metal must be 2 parts to pull the total 7 parts up to Rs. 80; this yields the ratio 1 : 4 : 2.

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