Question

50grams of an alloy of gold and silver contains 80% gold.the quantity of gold that is to be mixed up with this alloy so that it may contain 95% gold is options are (a)45gms,(b)150gms,(c)15gms and (d)50gms

Answer 1

Question:

50 grams of an alloy of gold and silver contains 80% gold. What the quantity of gold that is to be mixed up with this alloy so that it may contain 95% gold .

Options :

(a) 45 gms

(b) 150 gms

(c) 15 gms

(d) 50 gms

Answer:

Option:(b)

150 gms

Solution:

It is given that;

50 gms of an alloy of gold and silver contains 80% gold.

Thus,

Quantity of gold present in 50 gms alloy

= 80% of 50 gms

= (80/100)•50 gms

= 8•5 gms

= 40 gms

Now,

It is asked to mix some quantity of gold in the 50 gms of that alloy , so that the mixture may contain 95% gold.

Thus,

Let the quantity of the gold to be added be

x gms.

Hence,

The total quantity of mixture = (50+x) gms

Also,

The total quantity to gold in mixture = (40+x) gms

According to the question,

The new new mixture must contain 95% gold.

Thus,

=> (40+x)/(50+x) = 95/100

=> (40+x)/(50+x) = 19/20

=> (50+x-10)/(50+x) = (20-1)/20

=> (50+x)/(50+x) - 10/(50+x) = 20/20 - 1/20

=> 1 - 10/(50+x) = 1 - 1/20

=> - 10/(50+x) = - 1/20

=> 10/(50+x) = 1/20

=> 10•20 = 1•(50+x)

=> 200 = 50 + x

=> x = 200 - 50

=> x = 150 gms

Hence,

150 gms of gold should be added to 50 gram of the alloy so that the new mixture may contain 95% of gold.

Answer 2

${\large\bf{\mid{\overline{\underline{Given:-}}}\mid}}$

• Total Quantity of mixture = 50gram.
• Gold = 80%
• after mix more gold Gold = 95% .

$\Large\underline\mathfrak{Question}$

• we have to Find how much Quantity of gold was mixed ...

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$\Large\bold\star\underline{\underline\textbf{Solution(1)}}$

First lets try to solve it with basic method ..

initial gold was 80% in 50gm .

That means gold = 80*50/100 = 40gm .

Now, let x gram of gold was added .

than total Quantity = (50+x)

and total gold = (40+x) .

it is given , this is 95% this times .

so,

$\frac{(40 + x) \times 100}{(50 + x)} = 95 \\ \\ \red\leadsto \: 4000 + 100x = 4750 + 95x \\ \\ \red\leadsto \: 100x - 95x = 4750 - 4000 \\ \\ \red\leadsto \: 5x = 750 \\ \\ \red\leadsto \: x = \frac{750}{5} \\ \\ \red\leadsto \: x = 150$

Hence, 150gm of Gold was added .....

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$\Large\bold\star\underline{\underline\textbf{Solution(2)}}$

lets try it with ratio method now ,,

→ initial gold silver % = 80 : 20 = 4 : 1

Final gold and silver % = 95 : 5 = 19 : 1 ..

4 : 1

19:1

(19-4) = 15 unit ,,,

inital (4+1) = 5 unit is Equal to = 50gm ..

so,

15 unit is equal to = 50*15/5 = 150gm ....

Hence , gold added was 150gm.....

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