Percentage problem

Expert replies

seema19: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Sep 14, 2011 12:34 am

by seema19 » Sun Oct 02, 2011 9:00 am

An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that the percentage of gold is increased to 90?

a. 50
b. 60
c. 30
d. 40
e. 10

Ans: A
Can someone please let me know how to solve pbms like this.

Like this post

Source: Beat The GMAT — Problem Solving | Sun Oct 02, 2011 9:00 am

GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Sun Oct 02, 2011 9:34 am

You start with 50 grams of 80% gold. As you add pure gold, the overall percentage of gold increases. As you keep adding gold it will keep increasing to 100% (but it will never actually be 100% because you'll always have your original 50 grams of impure gold in the mix). When you mix two things together like this, the overall percentage will be weighted toward the one that makes up the majority of the mixture. For example, if we only add a tiny bit of 100% gold, the overall percentage would be very close to 80 because the 80% gold is dominating the mixture. If we had tons of 100% gold, the overall percentage would be very close to 100% because now the pure gold is dominating the mixture.

In this case, we want the percentage to be 90, which is right in the middle of 80 and 100. To achieve this, the amount of the 80% and 100% gold would have to be exactly equal. So that is why it should be 50 grams.

Now let's look at a more complicated example: the case where we want the overall percentage to be 95%. Notice that 95 is 3/4 of the way from 80 to 100. If we add enough of the 100% gold so that it pulls the overall percentage 3/4 of the way from 80 to 100, then it must make up 3/4 of the mixture. If it is 3/4 of the mixture there must be 3 parts 100% gold per 1 part 80% gold, a 3:1 ratio, so you would need to add 150 grams.

Of course, there is also the old-fashioned way to calculate it:

%=100*(amount of gold)/(total weight). Amount of gold in 50 grams of 80% gold is .8*50=40. If we add x grams of pure gold, the total amount of gold would be 40+x, and the total weight would be 50+x.

we want this to equal 90%, so solve: (40+x)/(50+x)=0.9 to get [spoiler]x=50[/spoiler]

Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial

Like this post

Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sun Oct 02, 2011 9:37 am

seema19 wrote:An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that the percentage of gold is increased to 90?

a. 50
b. 60
c. 30
d. 40
e. 10

Ans: A
Can someone please let me know how to solve pbms like this.

Total Quantity is 50gm

Gold is = 40gm

silver = 10 gm

Now we are adding some gold to the existing alloy...

hence there will be an increase in Quantity of the Alloy as well as an increase in % of Gold in the allow. This will give rise to an increase in % of gold in the allow to 90% of the Allow...

Let the quantity of Gold added be x...

So , X + 40 / ( 50 + X ) = 9 / 10 {% of gold to the Allow is 90%}

Or, 10x + 400 = 450 + 9x

So , x = 50

Hence 50gms of gold must be added to the allow..

Abhishek

Like this post

sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Sun Oct 02, 2011 10:17 am

GmatMathPro wrote:You start with 50 grams of 80% gold. As you add pure gold, the overall percentage of gold increases. As you keep adding gold it will keep increasing to 100% (but it will never actually be 100% because you'll always have your original 50 grams of impure gold in the mix). When you mix two things together like this, the overall percentage will be weighted toward the one that makes up the majority of the mixture. For example, if we only add a tiny bit of 100% gold, the overall percentage would be very close to 80 because the 80% gold is dominating the mixture. If we had tons of 100% gold, the overall percentage would be very close to 100% because now the pure gold is dominating the mixture.

In this case, we want the percentage to be 90, which is right in the middle of 80 and 100. To achieve this, the amount of the 80% and 100% gold would have to be exactly equal. So that is why it should be 50 grams.

Now let's look at a more complicated example: the case where we want the overall percentage to be 95%. Notice that 95 is 3/4 of the way from 80 to 100. If we add enough of the 100% gold so that it pulls the overall percentage 3/4 of the way from 80 to 100, then it must make up 3/4 of the mixture. If it is 3/4 of the mixture there must be 3 parts 100% gold per 1 part 80% gold, a 3:1 ratio, so you would need to add 150 grams.

Of course, there is also the old-fashioned way to calculate it:

%=100*(amount of gold)/(total weight). Amount of gold in 50 grams of 80% gold is .8*50=40. If we add x grams of pure gold, the total amount of gold would be 40+x, and the total weight would be 50+x.

we want this to equal 90%, so solve: (40+x)/(50+x)=0.9 to get [spoiler]x=50[/spoiler]

In your second example after arriving at the ratio of 3:4. How did you arrive at 150gm? Shouldn't it be 3/4*(100) = 75 gms?

Like this post

mad2011: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon Aug 29, 2011 4:42 am; Thanked: 1 times

by mad2011 » Mon Oct 03, 2011 1:19 am

I don't have a systematic method but this is how I did it

80% of 50Gms is Gold

GOLD =40 Gms Silver 10 Gms
now we are not changing Sliver portions so we need 9 times gold to make it 90%
90Gms -40gms = 50gms

Like this post

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Mon Oct 03, 2011 2:23 am

seema19 wrote:An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that the percentage of gold is increased to 90?

a. 50
b. 60
c. 30
d. 40
e. 10

Ans: A
Can someone please let me know how to solve pbms like this.

As the explanations above show, the math is confusing here. Go for reverse Plugging in: plug the answer choices into the question, see of adding the quantity in answer choice A, B, C, D, E leads you to a 90% gold alloy.

Try A:

If we add 50 grams to a 50 gram alloy, we are left with 100 grams, out of which 40+50=90 grams are gold. Is 90 grams 90% of 100? Indeed they are. So we plugged in answer choice A and everything checks out - therefore A is the right answer.

If you were to plug in any other answer choice, you would not reach 90% (otherwise there would be two right answer choices here). Thus, there's no need to test any of the others.

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Oct 03, 2011 2:52 am

seema19 wrote:An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that the percentage of gold is increased to 90?

a. 50
b. 60
c. 30
d. 40
e. 10

Ans: A
Can someone please let me know how to solve pbms like this.

This is a weighted average question.
Almost no math is needed if we understand how weighted averages work.

We need to combine 80% gold with 100% gold to yield a mixture that is 90% gold.
Since 90 is halfway between 80 and 100, equal amounts of the 80% gold and the 100% gold are needed.
Thus, the 50gms of the 80% gold must be combined with 50gms of the 100% gold.

The correct answer is A.

Other mixture problems:

https://www.beatthegmat.com/mixture-prob ... 89508.html

https://www.beatthegmat.com/problem-from ... 49413.html

https://www.beatthegmat.com/mixture-t76266.html

https://www.beatthegmat.com/mixture-t78188.html

https://www.beatthegmat.com/sugar-mixtures-t87858.html

https://www.beatthegmat.com/alchol-and-w ... 90495.html

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review