IIMB 2001 (QA) PYQs

A sum of $₹7,740$ is divided between X, Y, and Z such that the ratio of the share of X to the combined share of Y and Z is $4 : 11$ and the ratio of the share of Z to the combined share of X and Y is $1 : 3$. What is the share (in Rs.) of Y?

There are three containers $x,y,z$. In container $x$, the ratio of milk and water is $2:1$, in container $y$ the ratio of water and milk is $2:a$. If container $x$ and $y$ are mixed in the ratio of $2:3$, to get $100$ litres of a mixture having milk and water in the ratio $3:1$. Find the value of $a.$

Two iron alloys have different iron percentages. The first alloy weighs $6$ kg and the second weighs $12$ kg. Equal-weight pieces were cut from both alloys. Each piece was then added to the other alloy, resulting in the same iron percentage in both new alloys. What was the weight of each cut-off piece?