VeritasKarishma wrote:
nitesh50 wrote:
Hi
VeritasKarishmahttps://gmatclub.com/forum/a-coin-made- ... 98446.htmlYou have posted a reply for this question.
In your solution you have asked:
(Think what would happen if it was given that volume of aluminium was twice the volume of silver)
IMO the ratio for the weight will still remain the same.
Aluminium=10 Silver=20
ON the other hand 2/3 of volume of the coin will be aluminium.
Then we can use proportions :
If 2/3 Volume of C1 = 10gm
Then volume of C2= 10*1.5*volume of c2/volume of c1
This have me an answer of 30gm.
Am I correct here?
Regards
Nitesh
That solution can be modified if we modify the question like this:
A coin made of alloy of aluminum and silver measures 2 x 15 mm. If the weight of the coin is 30 grams and the volume of aluminum in the alloy is twice that of silver, what will be the weight of a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum?
Let's consider the first coin:
2*Volume of Silver = Volume of Aluminium
Weight of Silver = 2* Weight of Aluminum for equal volume.
Since the volume of silver is half but its weight is twice for equal volume so for half the volume, the weight of the two will become equal.
Total weight is 30 gms. So silver must be 15 gms and aluminum must be 15 gms. Volume of first coin \(=\pi∗(15/2)^2∗2=(225/2)∗\pi\)
Volume of second coin \(=\pi∗(15)^2∗1=(225)∗\pi\)
Volume of second coin is twice the volume of the first coin. If volume of aluminium in the first coin is V, the volume of the first coin is (3/2)V. The volume of the second coin is 3V. Since it is all Aluminium, volume of Aluminium in the second coin is 3V.
Since weight of Aluminum of weight V was 10 gms, weight of Aluminum of volume 3V will be 30 gms.Hi Karishma
VeritasKarishma,
Can you please clarify the below points regarding this modified question?
1) The net effect of the two things (I am calling them 'a' and 'b', below):
a) The volume of aluminum in the alloy is twice that of silver
b) The silver is twice as heavy as aluminum (meaning the weight of silver in the alloy is twice that of aluminium)
is that
the weight of aluminium in the alloy has become equal to that of silver,
each is 15 g now? (I have also highlighted this in Magenta in your reply).
Then what does the statement "The silver is twice as heavy as aluminum" signifies?? Haven't we contradicted the given statement?
2) If the weight of Aluminium in the alloy is 15 g (as you have shown in above reply), then the final answer in this question would be
15 * 3 = 45 g, as per my understanding. (I have also highlighted this in Red in your reply).
I'm very much clear about the original question as you have explained in the link:
https://gmatclub.com/forum/a-coin-made- ... ml#p974280But, I'm confused on this modified question. Please clarify if possible.
TIA.
Regards,
Ravish.