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 ₹).

How many $kg$ of sugar costing ₹ $5.50$ per $kg$ must be mixed with $60 \ kg$ of sugar costing ₹ $4.80$ per $kg$ so that the mixture is worth ₹ $5.25$ per $kg$?

$A$ container contains $50 \, \text{litres}$ of milk. From this container $5 \, \text{litres}$ of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container? (in $\text{litres}$)

$A$ person covers a distance of $100\, km$ in $10\, hours$,partly by walking at $7\, km/h$ and the rest by running at $12\, km/h$. Find out the distance covered in each part (in $km$).

$A$ trader has $50 \text{ kg}$ 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 and $5 \%$ loss? (in $\text{kg}$)

$A$ 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?