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kiran120680
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There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10% 21 Jun 2019, 10:40
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There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10%, 40% and 70% concentration of zinc respectively. If p grams of M1, q grams of M2 and r grams of M3 is mixed to form (p +q+ r) grams of mixture with 25% zinc concentration. What is the value r in terms of p and q?


A. (p−q)/3
B. (p−q)/2
C. (p+q)/2
D. (p+q)/3
E. (p+2q)/3
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A
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nick1816
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There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10% 21 Jun 2019, 12:25
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In p grams of M1, amount of zinc= 0.1p
In q grams of M2, amount of zinc= 0.4q
In q grams of M3, amount of zinc= 0.7r

\(\frac{0.1p+ 0.4q + 0.7r}{p+q+r}=\frac{1}{4}\)

0.6p=0.6q+1.8r
p=q+3r
r=1/3*(p-q)


kiran120680
There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10%, 40% and 70% concentration of zinc respectively. If p grams of M1, q grams of M2 and r grams of M3 is mixed to form (p +q+ r) grams of mixture with 25% zinc concentration. What is the value r in terms of p and q?


A. (p−q)/3
B. (p−q)/2
C. (p+q)/2
D. (p+q)/3
E. (p+2q)/3
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There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10% 10 May 2021, 22:30
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nick1816
In p grams of M1, amount of zinc= 0.1p
In q grams of M2, amount of zinc= 0.4q
In q grams of M3, amount of zinc= 0.7r

\(\frac{0.1p+ 0.4q + 0.7r}{p+q+r}=\frac{1}{4}\)

0.6p=0.6q+1.8r
p=q+3r
r=1/3*(p-q)


kiran120680
There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10%, 40% and 70% concentration of zinc respectively. If p grams of M1, q grams of M2 and r grams of M3 is mixed to form (p +q+ r) grams of mixture with 25% zinc concentration. What is the value r in terms of p and q?


A. (p−q)/3
B. (p−q)/2
C. (p+q)/2
D. (p+q)/3
E. (p+2q)/3
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nick.. can you suggest some good source of concept files for solving mixture problems.
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There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10% 11 May 2021, 00:26
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pandajee
nick1816
In p grams of M1, amount of zinc= 0.1p
In q grams of M2, amount of zinc= 0.4q
In q grams of M3, amount of zinc= 0.7r

\(\frac{0.1p+ 0.4q + 0.7r}{p+q+r}=\frac{1}{4}\)

0.6p=0.6q+1.8r
p=q+3r
r=1/3*(p-q)


kiran120680
There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10%, 40% and 70% concentration of zinc respectively. If p grams of M1, q grams of M2 and r grams of M3 is mixed to form (p +q+ r) grams of mixture with 25% zinc concentration. What is the value r in terms of p and q?


A. (p−q)/3
B. (p−q)/2
C. (p+q)/2
D. (p+q)/3
E. (p+2q)/3


nick.. can you suggest some good source of concept files for solving mixture problems.
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18. Mixture Problems



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
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There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10% 12 Oct 2022, 23:01
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There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10%, 40% and 70% concentration of zinc respectively. If p grams of M1, q grams of M2 and r grams of M3 is mixed to form (p +q+ r) grams of mixture with 25% zinc concentration. What is the value r in terms of p and q?


A. (p−q)/3
B. (p−q)/2
C. (p+q)/2
D. (p+q)/3
E. (p+2q)/3

Using Weighted Average : Assume Volume of alloy = 100
10P + 40Q + 70R = 25(P+Q+R)
10P + 40Q + 70R = 25P + 25Q + 25R
Keep R terms in the RHS and equate.
70R - 25R = 25P - 10P + 25Q - 40Q
45R = 15P - 15Q (Divide both sides by 15)
3R = P - Q
R =\((P - Q)/(3)\)
\(A\)
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There are three types of zinc-aluminium alloy, M1, M2 and M3, with 10% 13 Apr 2026, 08:42
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Deconstructing the Question

The three alloys have zinc concentrations \(10\%\), \(40\%\), and \(70\%\).

We mix \(p\) grams of M1, \(q\) grams of M2, and \(r\) grams of M3 to get a final mixture with \(25\%\) zinc.

We set up an equation using total zinc.

Step-by-step

Zinc from M1 is

\(\frac{1}{10}p\)

Zinc from M2 is

\(\frac{2}{5}q\)

Zinc from M3 is

\(\frac{7}{10}r\)

Total mixture is

\(p+q+r\)

Since the final concentration is \(\frac{1}{4}\), total zinc is

\(\frac{1}{4}(p+q+r)\)

So

\(\frac{1}{10}p + \frac{2}{5}q + \frac{7}{10}r = \frac{1}{4}(p+q+r)\)

Multiply through by \(20\):

\(2p + 8q + 14r = 5p + 5q + 5r\)

Rearrange:

\(14r - 5r = 5p - 2p + 5q - 8q\)

\(9r = 3p - 3q\)

\(9r = 3(p-q)\)

\(r = \frac{p-q}{3}\)

Answer: A
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