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 cask to that of water is 16 : 65. How much wine did the cask hold originally?

A. 18 litres B. 24 litres C. 32 litres D. 42 litres Answer: Option B
Show Answer

Solution(By Apex Team)

Let the quantity of the wine in the cask originally be x litres. Then, quantity of wine left in cask after 4 operations $\begin{aligned}&=\left[x\left(1-\frac{8}{x}\right)^4\right]\text{ litres }\\ &\therefore\left(\frac{x\left(1-\left(\frac{8}{x}\right)\right)^4}{x}\right)=\frac{16}{81}\\ &\Rightarrow\left(1-\frac{8}{x}\right)^4=\left(\frac{2}{3}\right)^4\\ &\Rightarrow\frac{x-8}{x}=\frac{2}{3}\\ &\Rightarrow3x-24=2x\\ &\Rightarrow x=24\text{ litres }\end{aligned}$

Related Questions On Alligation

The ratio, in which tea costing Rs. 192 per kg is to be mixed with tea costing Rs. 150 per kg so that the mixed tea when sold for Rs. 194.40 per kg, gives a profit of 20%.

A. 2 : 5
B. 3 : 5
C. 5 : 3
D. 5 : 2
Show Answer

An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be:

A. $\large\frac{1}{2} \mathrm{~kg}$
B. $\large\frac{1}{8} \mathrm{~kg}$
C. $\large\frac{3}{14} \mathrm{~kg}$
D. $\large\frac{7}{9} \mathrm{~kg}$
Show Answer

In a 729 litres mixture of milk and water, the ratio of milk to water is 7 : 2. to get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is:

A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres
Show Answer

In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

A. 1 : 2
B. 1 : 3
C. 2 : 1
D. 3 : 1
Show Answer

More Related Questions On Alligation

प्रातिक्रिया दे