$A$ 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 $Rs.$)

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

$A$ trader has $50 \ kg$ of sugar,a part of which he sells at $10 \%$ profit and the rest at $5 \%$ loss. He gains $7 \%$ on the whole. What is the quantity sold at $10 \%$ gain and $5 \%$ loss? (in $kg$)

$A$ tea seller mixes three qualities of tea $T_{1}, T_{2}$,and $T_{3}$ priced at $Rs. 74$ per kg,$Rs. 68$ per kg,and $Rs. 63$ per kg in the ratio of $1:2:4$. He added some more quantity of $T_{1}$ to $4$ kg of this mixture. He sold this new mixture for $Rs. 84$ per kg,thereby making a profit of $20\%$. How much of $T_{1}$ did he mix with the mixture? (in kg)

The ratio of the quantities of an acid and water in a mixture is $1:3$. If $5$ $litres$ of acid is further added to the mixture,the new ratio becomes $1:2$. The quantity of the new mixture in litres is

In what ratio must oil at $Rs. 62$ per $kg$ be mixed with oil at $Rs. 72$ per $kg$ so that the mixture is worth $Rs. 64.50$ per $kg$?