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A jeweler has bars of 18-carat gold and 12- carat gold. How much of each must be melted

together to obtain a bar of 16-carat gold weighing 120 grams? (Pure gold is 24 carat)

Answer:

Let’s assume the quantity of 18-carat gold as x gm and 12-carat gold as y gm.

Then according to the first condition given in the problem, we have

x + y = 120 … (i)

Pure gold is 24 carat

So, the purity of 18-carat gold = (18/24) x 100%

= (¾) x 100

= 75%

Purity of 12 carat gold = (12/24) x 100%

= ½ x 100%

= 50%

And, the purity of 16-carat gold = (16/24) x 100%

= (2/3) x 100%

= 200/3%

Now, according to the second condition given in the problem, we have

75x + 50y = 200/3 x 120

75x + 50y = 200 x 40

75x + 50y = 8000

3x + 2y = 320 … (ii)

Performing (ii) – 2 x (i), we get

3x + 2y = 320

2x + 2y = 240

(-)—(-)—(-)---

x = 80

On substituting the value of x in equation (i), we get

80 + y = 120

y = 120 – 80

y = 40

Therefore, the jeweler requires 80 gm of 18-carat gold and 40 gm of 12-carat gold to obtain a bar of 16

carat gold weighing 120 gm.

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