Shyam Saraf and Abhilasha Swarup Solutions for Exercise 1: EXERCISE

A bartender steals $20$ litres of wine from a cask full of wine and replaces it with water. He repeats the process two more times. What is the volume of the cask if the ratio of wine to water in the final solution is $64: 61$ ?

A bartender steals $45$ litres of wine from a cask full of wine and replaces it with water. He repeats the process one more time. What is the volume of the cask if the ratio of wine to water in the final solution is $16 : 9$?

A cloth merchant bought $3,000$ m of cloth. He sells part of the stock at $3\%$ loss and the remaining at $12\%$ profit. If he made an overall profit of $10\%$, then how many metres of cloth was sold at a loss?

A jar containing a mixture of wine and soda has $60\%$ wine. A part of this mixture was replaced by another mixture of wine and soda having $45\%$ soda. The mixture now has $53\%$ wine. Find out what percentage of the jar was replaced.

A vessel is completely filled with $150$ litres of wine. First, $15$ litres of wine is taken out and replaced with water. Again, $15$ litres is taken out and replaced with water. How many minimum times should this process be carried out so that the quantity of wine becomes less than $100$ litres in the final mixture?

A vessel is filled with $150$ litres of a wine and water solution in the ratio of $2:1.$ First, $15$ litres of wine is taken out and replaced with water. Again, $15$ litres is taken out and replaced with water. How many minimum times should this process be carried out so that the quantity of wine becomes less than $75$ litres in the final mixture?

What quantity of a $90\%$ wine solution should be mixed with $40$ ml of a $35\%$ wine solution in order to get a$50\%$ wine solution?

The ratio of milk and water in three completely-filled bottles of the same volume is $1 : 1, 2 : 1,$and $3 : 2$. If the three bottles are mixed in a larger vessel, then the ratio of milk and water in larger vessel is _____.