$A$ 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 $kg$):

$A$ tub contains a mixture of two liquids $P$ and $Q$ in the ratio of $4:1$. When $10 \, L$ of the mixture is taken out and $10 \, L$ of liquid $Q$ is poured into the tub,the ratio becomes $2:3$. How many litres of liquid $P$ were contained in the tub initially?

$A$ 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 $\text{kg}$)

In what ratio must $25 \%$ hydrochloric acid be mixed with $60 \%$ hydrochloric acid to get a mixture of $40 \%$ hydrochloric acid?

How much water should be added to $14$ litres of milk worth ₹ $5.40$ a litre so that the value of the mixture may be ₹ $4.20$ a litre? (in litres)

$A$ dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains $25 \%$. The percentage of water in the mixture is?