In what ratio must a grocer mix two varieties of pulses costing ₹ $15$ and ₹ $20$ per $kg$ respectively so as to get a mixture worth ₹ $16.5/kg$?

Two alloys contain tin and iron in the ratio of $1:2$ and $2:3$. If the two alloys are mixed in the proportion of $3:4$ respectively (by weight),the ratio of tin and iron in the newly formed alloy is:

$A$ mixture contains $80 \%$ acid and the rest water. What part of the mixture should be removed and replaced by the same amount of water to make the ratio of acid to water $4:3$?

In what ratio must water be added to spirit to gain $10 \%$ by selling it at the cost price?

$A$ shopkeeper bought $20 \ kg$ of onions at $Rs. 6.50$ per $kg$ and $30 \ kg$ of onions at $Rs. 7$ per $kg$. He sold the mixture at a total profit of $Rs. 60$. At what price per $kg$ did he sell the mixture of onions? (in $Rs.$)

$20$ litres of a mixture contains $20 \%$ alcohol and the rest is water. If $4$ litres of water are added to it,what will be the percentage of alcohol in the new mixture?