Some amount out of ₹$7000$ was lent at $6 \%$ $p.a.$ and the remaining at $4 \%$ $p.a.$ If the total simple interest from both the fractions in $5$ $years$ was ₹$1600$,the sum lent at $6 \%$ $p.a.$ was (in ₹).

Two types of alloys contain gold and silver in the ratio of $7: 22$ and $21: 37.$ In what ratio should these alloys be mixed,so as to have a new alloy in which gold and silver would exist in the ratio $25: 62?$

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

$A$ jar contained a mixture of two liquids $A$ and $B$ in the ratio $3 : 2.$ When $5$ litres of the mixture was taken out and $5$ litres of liquid $B$ was poured in the jar,this ratio became $2 : 3.$ The quantity of liquid $A$ contained in the jar initially was (in litres).

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 $kg$)

$A$ mixture of $80$ litre of milk and water contains $10 \%$ water. How much water must be added to make $20 \%$ water in the new mixture? (in $litre$)