How many $kg$ of salt at $42$ $P$ per $kg$ must a man mix with $25 \, kg$ of salt at $24$ $P$ per $kg$,so that he may,on selling the mixture at $40$ $P$ per $kg$,gain $25 \%$ on the outlay?

In $50\, g$ alloy of gold and silver,the gold is $80\%$ by weight. How much gold should be mixed to this alloy,so that the weight of gold would become $95\%$? (in $g$)

In what proportion must pulses of $Rs. 70$ per $kg$ be mixed with pulses of $Rs. 45$ per $kg$ to get a mixture of $Rs. 60$ per $kg$?

$A$ trader has $50 \text{ kg}$ of pulses,part of which he sells at $8 \%$ profit and the rest at $18 \%$ profit. He gains $14 \%$ on the whole. What is the quantity sold at $18 \%$ profit? (in $\text{kg}$)

$A$ man has given ₹ $300000$ as a loan. He lent some of his capital to Ajay at an interest rate of $20 \%$ per annum and the rest to Ramesh at an interest rate of $12 \%$ per annum. At the end of one year,he received $17 \%$ of his total capital as interest. How much did he lend to Ajay? (in ₹)

Milk and water are mixed in vessel $A$ in the ratio of $5:2$ and in vessel $B$ in the ratio of $8:5$. In what ratio should quantities be taken from the two vessels so as to form a mixture in which milk and water will be in the ratio of $9:4$?