Question

A jeweller 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 1

Heya! !!!

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Let x g and y g be the weight of 18-carat and 12-carat gold respectively.

As per the given condition

(18x/24)+(12y/24) = (120×16)/24

⇒3x+2y=320                                            .....(i)

And
x+y=120                                                    .....(ii)

Multiplying (ii) by 2 and subtracting from (i), we get

x=320−240=80

Now, putting x = 80 in (ii), we have

80+y=120⇒y=40

Hence, the required weight of 18-carat and 12-carat gold bars are 80 g and 40 g respectively.

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Hope it will help u !!!

Cheers ☺☺

# Nikky

Answer 2

Answer:

Let the 18-carat gold be=x gm,and 12-carat gold be=y gm,then

x+y=120---------1)

18x+12y=16×120

3x+2y=320--------2)

Multiply eq.1 by 3

3x+3y=360(on subtracting)

3x+2y=320

- - -

y=40(grams)

Put y=40 in Eq.1)

x+40=120

x=120-40

x=80 (grams)

Thus, 18 carat gold must be melted 80 grams and 12 carat gold must be melted 40 grams.

Step-by-step explanation:

As above