How many kg of sugar costing ₹ $11.70/kg$ must be mixed with $24$ $kg$ of sugar costing ₹ $8.1/kg$ so that there may be a gain of $15 \%$ by selling the mixture at ₹ $9/kg$? (in $kg$)

$A$ merchant has $1000 \ kg$ of rice,part of which he sells at $8 \%$ profit and the rest at $16 \%$ profit. He gains $14 \%$ on the whole. The quantity sold at $16 \%$ profit is (in $kg$):

Three boxes of capacity $24\, kg$,$36\, kg$,and $84\, kg$ are completely filled with three varieties of wheat $A$,$B$,and $C$ respectively. All three boxes were emptied,the three types of wheat were thoroughly mixed,and the mixture was put back into the three boxes. How many $kg$ of type $A$ wheat would be there in the third box?

$A$ shopkeeper bought $30 \text{ kg}$ of rice at the rate of $₹ 70$ per $\text{kg}$ and $20 \text{ kg}$ of rice at the rate of $₹ 70.75$ per $\text{kg}$. If he mixed the two brands of rice and sold the mixture at $₹ 80.50$ per $\text{kg}$,his total gain is (in $₹$):

$A$ shopkeeper has $50 \ kg$ of rice,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?

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?