Strength of salt in a mixture is p%. Various concentration of slats are added
$begingroup$
The strength of a salt solution is $p$% if $100$ ml of the solution contains $p$ grams of salt. If three salt solutions A, B, C are mixed in the proportion $1 : 2: 3$, then the resulting solution has strength $20$%. If instead, the proportion is $3 : 2: 1$, then the resulting solution has strength $30$%. A fourth solution, D, is produced by mixing B and C in the ratio $2: 7$. The ratio of the strength of D to that of A is
1) $2:5$
2) $3:10$
3) $1:4$
4) $1:3$
My attempt:
Let's say A has $a$%, B has $b$% and C has $c$%. And we take $1$, $2$ and $3$ kgs of them respectively. This will give us $20$% solution.
Therefore, $frac{a}{100}$+$frac{2b}{100}+frac{3c}{100}$=$1.2$ kgs
This means $a+2b+3c=120$…(1)
Similarly $frac{3a}{100}+frac{2b}{100}+frac{c}{100}$=$1.8$ kgs
So, $3a+2b+c=180$…(2)
Adding (1) and (2) we get, $a+b+c=75$ and subtracting them we get $a-c=30$. How to proceed further?
percentages ratio
edited Dec 20 '18 at 14:05
saulspatz
14.5k21329
asked Dec 20 '18 at 13:55
Sherlock WatsonSherlock Watson
3462413
$endgroup$
add a comment |
$begingroup$
The strength of a salt solution is $p$% if $100$ ml of the solution contains $p$ grams of salt. If three salt solutions A, B, C are mixed in the proportion $1 : 2: 3$, then the resulting solution has strength $20$%. If instead, the proportion is $3 : 2: 1$, then the resulting solution has strength $30$%. A fourth solution, D, is produced by mixing B and C in the ratio $2: 7$. The ratio of the strength of D to that of A is
1) $2:5$
2) $3:10$
3) $1:4$
4) $1:3$
My attempt:
Let's say A has $a$%, B has $b$% and C has $c$%. And we take $1$, $2$ and $3$ kgs of them respectively. This will give us $20$% solution.
Therefore, $frac{a}{100}$+$frac{2b}{100}+frac{3c}{100}$=$1.2$ kgs
This means $a+2b+3c=120$…(1)
Similarly $frac{3a}{100}+frac{2b}{100}+frac{c}{100}$=$1.8$ kgs
So, $3a+2b+c=180$…(2)
Adding (1) and (2) we get, $a+b+c=75$ and subtracting them we get $a-c=30$. How to proceed further?
percentages ratio
edited Dec 20 '18 at 14:05
saulspatz
14.5k21329
asked Dec 20 '18 at 13:55
Sherlock WatsonSherlock Watson
3462413
$endgroup$
add a comment |
$begingroup$
The strength of a salt solution is $p$% if $100$ ml of the solution contains $p$ grams of salt. If three salt solutions A, B, C are mixed in the proportion $1 : 2: 3$, then the resulting solution has strength $20$%. If instead, the proportion is $3 : 2: 1$, then the resulting solution has strength $30$%. A fourth solution, D, is produced by mixing B and C in the ratio $2: 7$. The ratio of the strength of D to that of A is
1) $2:5$
2) $3:10$
3) $1:4$
4) $1:3$
My attempt:
Let's say A has $a$%, B has $b$% and C has $c$%. And we take $1$, $2$ and $3$ kgs of them respectively. This will give us $20$% solution.
Therefore, $frac{a}{100}$+$frac{2b}{100}+frac{3c}{100}$=$1.2$ kgs
This means $a+2b+3c=120$…(1)
Similarly $frac{3a}{100}+frac{2b}{100}+frac{c}{100}$=$1.8$ kgs
So, $3a+2b+c=180$…(2)
Adding (1) and (2) we get, $a+b+c=75$ and subtracting them we get $a-c=30$. How to proceed further?
percentages ratio
edited Dec 20 '18 at 14:05
saulspatz
14.5k21329
asked Dec 20 '18 at 13:55
Sherlock WatsonSherlock Watson
3462413
$endgroup$
The strength of a salt solution is $p$% if $100$ ml of the solution contains $p$ grams of salt. If three salt solutions A, B, C are mixed in the proportion $1 : 2: 3$, then the resulting solution has strength $20$%. If instead, the proportion is $3 : 2: 1$, then the resulting solution has strength $30$%. A fourth solution, D, is produced by mixing B and C in the ratio $2: 7$. The ratio of the strength of D to that of A is
1) $2:5$
2) $3:10$
3) $1:4$
4) $1:3$
My attempt:
Let's say A has $a$%, B has $b$% and C has $c$%. And we take $1$, $2$ and $3$ kgs of them respectively. This will give us $20$% solution.
Therefore, $frac{a}{100}$+$frac{2b}{100}+frac{3c}{100}$=$1.2$ kgs
This means $a+2b+3c=120$…(1)
Similarly $frac{3a}{100}+frac{2b}{100}+frac{c}{100}$=$1.8$ kgs
So, $3a+2b+c=180$…(2)
Adding (1) and (2) we get, $a+b+c=75$ and subtracting them we get $a-c=30$. How to proceed further?
percentages ratio
percentages ratio
edited Dec 20 '18 at 14:05
saulspatz
14.5k21329
asked Dec 20 '18 at 13:55
Sherlock WatsonSherlock Watson
3462413
edited Dec 20 '18 at 14:05
saulspatz
14.5k21329
asked Dec 20 '18 at 13:55
Sherlock WatsonSherlock Watson
3462413
edited Dec 20 '18 at 14:05
saulspatz
14.5k21329
edited Dec 20 '18 at 14:05
saulspatz
14.5k21329
edited Dec 20 '18 at 14:05
saulspatz
14.5k21329
14.5k21329
asked Dec 20 '18 at 13:55
Sherlock WatsonSherlock Watson
3462413
asked Dec 20 '18 at 13:55
Sherlock WatsonSherlock Watson
3462413
asked Dec 20 '18 at 13:55
Sherlock WatsonSherlock Watson
3462413
3462413
add a comment |
add a comment |
1 Answer
1
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$begingroup$
$a+b+c=75$ & $a−c=30$ give $c=a-30$ and $b=105-2a$.
Required ratio:
$$frac{2b+7c}{9a}=frac{210-4a+7a-210}{9a}=1:3$$
answered Dec 20 '18 at 14:04
Ankit KumarAnkit Kumar
1,384220
$endgroup$
1
$begingroup$
So simple and great.
$endgroup$
– Sherlock Watson
Dec 20 '18 at 15:05
$begingroup$
@SherlockWatson Thank you :)
$endgroup$
– Ankit Kumar
Dec 20 '18 at 15:07
add a comment |
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1 Answer
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1 Answer
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$begingroup$
$a+b+c=75$ & $a−c=30$ give $c=a-30$ and $b=105-2a$.
Required ratio:
$$frac{2b+7c}{9a}=frac{210-4a+7a-210}{9a}=1:3$$
answered Dec 20 '18 at 14:04
Ankit KumarAnkit Kumar
1,384220
$endgroup$
1
$begingroup$
So simple and great.
$endgroup$
– Sherlock Watson
Dec 20 '18 at 15:05
$begingroup$
@SherlockWatson Thank you :)
$endgroup$
– Ankit Kumar
Dec 20 '18 at 15:07
add a comment |
$begingroup$
$a+b+c=75$ & $a−c=30$ give $c=a-30$ and $b=105-2a$.
Required ratio:
$$frac{2b+7c}{9a}=frac{210-4a+7a-210}{9a}=1:3$$
answered Dec 20 '18 at 14:04
Ankit KumarAnkit Kumar
1,384220
$endgroup$
1
$begingroup$
So simple and great.
$endgroup$
– Sherlock Watson
Dec 20 '18 at 15:05
$begingroup$
@SherlockWatson Thank you :)
$endgroup$
– Ankit Kumar
Dec 20 '18 at 15:07
add a comment |
$begingroup$
$a+b+c=75$ & $a−c=30$ give $c=a-30$ and $b=105-2a$.
Required ratio:
$$frac{2b+7c}{9a}=frac{210-4a+7a-210}{9a}=1:3$$
answered Dec 20 '18 at 14:04
Ankit KumarAnkit Kumar
1,384220
$endgroup$
$a+b+c=75$ & $a−c=30$ give $c=a-30$ and $b=105-2a$.
Required ratio:
$$frac{2b+7c}{9a}=frac{210-4a+7a-210}{9a}=1:3$$
answered Dec 20 '18 at 14:04
Ankit KumarAnkit Kumar
1,384220
answered Dec 20 '18 at 14:04
Ankit KumarAnkit Kumar
1,384220
answered Dec 20 '18 at 14:04
Ankit KumarAnkit Kumar
1,384220
answered Dec 20 '18 at 14:04
Ankit KumarAnkit Kumar
1,384220
1,384220
1
$begingroup$
So simple and great.
$endgroup$
– Sherlock Watson
Dec 20 '18 at 15:05
$begingroup$
@SherlockWatson Thank you :)
$endgroup$
– Ankit Kumar
Dec 20 '18 at 15:07
add a comment |
1
$begingroup$
So simple and great.
$endgroup$
– Sherlock Watson
Dec 20 '18 at 15:05
$begingroup$
@SherlockWatson Thank you :)
$endgroup$
– Ankit Kumar
Dec 20 '18 at 15:07
1
1
$begingroup$
So simple and great.
$endgroup$
– Sherlock Watson
Dec 20 '18 at 15:05
$begingroup$
So simple and great.
$endgroup$
– Sherlock Watson
Dec 20 '18 at 15:05
$begingroup$
@SherlockWatson Thank you :)
$endgroup$
– Ankit Kumar
Dec 20 '18 at 15:07
$begingroup$
@SherlockWatson Thank you :)
$endgroup$
– Ankit Kumar
Dec 20 '18 at 15:07
add a comment |
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