$A$ 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 $km$).

$400 \, gm$ of salt solution has $40 \%$ salt in it. How much salt should be added to make the concentration $50 \%$ in the solution?

$A$ trader has $50 \ kg$ of sugar,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 $kg$)

There are $3$ tubs which contain mixtures of milk and water in the ratios of $5:2, 4:3,$ and $3:1$ respectively. If the mixtures are poured into a single tub,find the ratio of milk to water.

Three bottles of equal capacity contain mixtures of milk and water in the ratios $2:5$,$3:4$,and $4:5$ respectively. These three bottles are emptied into a large bottle. What will be the ratio of milk and water respectively in the large bottle?

An alloy is made by mixing metal $A$ costing ₹ $2000/kg$ and metal $B$ costing ₹ $400/kg$ in the ratio $A:B = 3:1$. What is the cost (in ₹) of $8$ kilograms of this alloy?