(B) Let the original quantity of wine be $x$ litres.After $1$ operation,the quantity of wine left is $x(1 - 8/x)$.After $4$ operations (the initial on

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(B) Let the original quantity of wine be $x$ litres.After $1$ operation,the quantity of wine left is $x(1 - 8/x)$.After $4$ operations (the initial one plus three more),the quantity of wine left is $x(1 - 8/x)^4$.The total volume of the mixture remains $x$ litres.The ratio of wine to water is $16:65$,so the ratio of wine to total mixture is $16:(16+65) = 16:81$.Thus,$\frac{x(1 - 8/x)^4}{x} = \frac{16}{81}$.$(1 - 8/x)^4 = (2/3)^4$.Taking the fourth root on both sides,$1 - 8/x = 2/3$.$8/x = 1 - 2/3 = 1/3$.$x = 8 \times 3 = 24$ litres.

Competitive Quantitative Aptitude Mixture and Alligation Mixture and Alligation

Medium

$8$ litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in the cask to that of water is $16:65$. How much wine did the cask hold originally? (in litres)

A
$18$
B
$24$
C
$32$
D
$42$

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Mixture and Alligation

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Mixture and Alligation

$A$ person has a chemical costing $Rs. 25$ per $litre$. In what ratio should water be mixed in the chemical so that by selling the mixture at $Rs. 20$ per $litre$,he may get a profit of $25\%$?

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$A$ person has ₹ $5000$. He invests a part of it at $3 \%$ per annum and the remainder at $8 \%$ per annum simple interest. His total income in $3$ years is ₹ $750$. Find the sum invested at different rates of interest (in ₹).

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Varun's expenditures and savings are in the ratio of $4:1$. His income increases by $20\%$. If his savings increase by $12\%$, by how much percentage should his expenditure increase?

Medium

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$A$ person has $60$ pens. He sells some of these at a profit of $12 \%$ and the rest at $8 \%$ loss. On the whole,he gets a profit of $11 \%$. How many pens were sold at $12 \%$ profit and how many at $8 \%$ loss?

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Gold is $19$ times as heavy as water and copper is $9$ times as heavy as water. In what ratio should these metals be mixed so that the mixture may be $15$ times as heavy as water?

Medium

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$8$ litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in the cask to that of water is $16:65$. How much wine did the cask hold originally? (in litres)

Similar Questions

$A$ person has a chemical costing $Rs. 25$ per $litre$. In what ratio should water be mixed in the chemical so that by selling the mixture at $Rs. 20$ per $litre$,he may get a profit of $25\%$?

$A$ person has ₹ $5000$. He invests a part of it at $3 \%$ per annum and the remainder at $8 \%$ per annum simple interest. His total income in $3$ years is ₹ $750$. Find the sum invested at different rates of interest (in ₹).

Varun's expenditures and savings are in the ratio of $4:1$. His income increases by $20\%$. If his savings increase by $12\%$, by how much percentage should his expenditure increase?

$A$ person has $60$ pens. He sells some of these at a profit of $12 \%$ and the rest at $8 \%$ loss. On the whole,he gets a profit of $11 \%$. How many pens were sold at $12 \%$ profit and how many at $8 \%$ loss?

Gold is $19$ times as heavy as water and copper is $9$ times as heavy as water. In what ratio should these metals be mixed so that the mixture may be $15$ times as heavy as water?

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