Arun Sharma Solutions for Exercise 1: Level of Difficulty

Raman steals four gallons of liquid soap kept in a train compartment's bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals $4$gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it is found that the ratio of the liquid soap now left in the container to that of the water in it is $36: 13$. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?

Two vessels contain a mixture of spirit and water. In the first vessel the ratio of spirit to water is $8: 3$ and in the second vessel the ratio is $5: 1$. A $35$litre cask is filled from these vessels so as to contain a mixture of spirit and water in the ratio of $4: 1 .$ How many liters are taken from the first vessel?

There are two mixtures of milk and water, the quantity of milk in them being $20\%$ and $80\%$ of the mixture. If $2$liters of the first are mixed with three liters of the second, what will be the ratio of milk to water in the new mixture?

There are two kinds of alloys of silver and copper.The first alloy contains silver and copper such that $93.33$% of it is silver. In the second alloy there is $86.66$% silver. What weight of the first alloy should be mixed with the some weight of the second alloy as to make a $100$ kg mass containing $90$% of silver?

Two buckets of equal capacity are full of a mixture of milk and water. In the first, the ratio of milk to water is $1: 7$ and in the second it is $3: 8$. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of milk to water?

A milkman stole milk from a can that contained $50\%$ of milk and he replaced what he had stolen with milk having $20\%$ milk. The bottle then contained only $25\%$ milk. How much of the bottle did he steal?

Shruti possessing $₹10000$, lent a part of it at $5\%$ simple interest and the remaining at $20\%$ simple interest. Her total income after five years was $₹7500$. Find the sum lent at $20\%$ rate.

Sharman decides to travel $100 \mathrm{km}$ in $8 \mathrm{hours}$ partly by foot and partly on a bicycle, his speed on foot being $10 \mathrm{km}/\mathrm{hr}.$ and that on bicycle being $20 \mathrm{km}/\mathrm{hr}.$, what distance would he travel by foot?