$600 \, gm$ of sugar solution contains $40 \%$ sugar. How much sugar should be added to make the concentration $50 \%$ in the solution? (in $gm$)

Aditya and Sanjay started a business investing $45000$ and $30000$ respectively. What will be the ratio between their profit?

$A$ barrel contains a mixture of wine and water in the ratio $3:1$. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes $1:1$?

$A$ mixture contains wine and water in the ratio $3:2$ and another mixture contains them in the ratio $4:5$. How many litres of the latter must be mixed with $3 \, L$ of the former so that the resulting mixture may contain equal quantities of the wine and water? (in $L$)

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

Tea worth ₹ $126/kg$ and ₹ $135/kg$ are mixed with a third variety in the ratio $1:1:2$. If the mixture is worth ₹ $153/kg$,the price of the third variety per kg will be (in ₹):