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150 kg of alloy containing copper and zinc in the ratio 3 : 2 mixed with X kg of alloy containing copper and zinc in the ratio 2 : 3. If the overall alloy should contain copper between 45% to 55% , what can be minimum value of X ?

150 kg of alloy containing copper and zinc in the ratio 3 : 2 mixed with X kg of alloy containing copper and zinc in the ratio 2 : 3. If the overall alloy should contain copper between 45% to 55% , what can be minimum value of X ? Correct Answer 50 kg 

Given that:

Quantity of alloy = 150 kg

in this alloy copper and zinc ratio = 3 : 2

calculation:

If  overall alloy contain copper as 45%

(150 × 3/5 + 2X/5) = 45 % (150 + X)

⇒ (90 + 2X/5) = 9 (150 + X)/20

⇒ 1800 + 8X = 1350 + 9X

⇒ X = 450 kg

If overall alloy contain copper as 55%

(90 + 2X/5) = 55 (150 + X) / 100

⇒ 1800 + 8X = 1650 + 11X

⇒ x = 50 kg

∴  The minimum value of X is 50 kg.

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