IIMB 2001 (QA) PYQs

Vessel P contains a $540$ liters mixture of acetone and ethanol in the ratio of $4: 5$ and vessel $Q$ contains the mixture of acetone and ethanol in the ratio of $5: 7$. Vessel $R$ contains $90$ liters of ethanol and $60$ liters of acetone. If vessel $P$ and $Q$ mixtures are mixed with vessel $R$, then the quantity of the ethanol in the resultant mixture is $33.33 \%$ more than the quantity of acetone in the resultant mixture. Find the initial total quantity of vessel $Q$.

A tank contains $1,500 \mathrm{~L}$ of water and $20 \mathrm{~kg}$ of dissolved salt. Fresh water is entering the tank at $15 \mathrm{~L} / \mathrm{min}$, and the solution drains at a rate of $10 \mathrm{~L} / \mathrm{min}$. How much salt (in grams) is in the tank at $10$ minutes?

A vat contains a blend of two liquids, P and Q, in the ratio of $7:5.$ If $9$ liters of this blend are taken out and the vat is refilled with liquid Q, the new ratio of P to Q becomes $7:9.$ How many liters of liquid P were there in the vat initially?