IIMB 2002 (QA) PYQs

75 people are stranded on an island, and they have sufficient food for 100 days. After 10 days, two-third of the people separate from the group in search of a way out. After another 16 days, 25 people return. From this day on, how many days will the food last?

If $x - 2y + 4z = 6$, $3x + y + 5z = 4$ and $2x - y + 3z = 4$, then what is the value of $(2x – 3y + 5z)$?

If $x=2-\frac{1}{x}$; then find the value of $x^{12}-2 x^{6}+5$