Ratios & Percent (Advanced)

Harder items at competition-adjacent depth.

Phase 2 · SAT Math

Ratios & Percent: core idea

Successive percent change.

A quantity is increased by $20\%$ and then decreased by $20\%$ . Starting at $150$ , what is the final value?

Hint: Apply both multipliers. Answer: 144.

1. Two solutions are mixed: $30\%$ acid and $50\%$ acid. How many liters of $50\%$ solution must be added to $6$ liters of $30\%$ solution to make $40\%$ acid?
2. A store marks an item up $25\%$ then gives a $20\%$ discount. Relative to the original price, what is the percent change?
3. The ratio of adults to children is $7:4$ . After $15$ children arrive, the ratio is $7:5$ . How many adults were originally present?
4. A $500$ dollar salary gets a $10\%$ raise followed by a $10\%$ raise. What is the new salary?
5. A $12$ % salt solution is diluted with water to make $8$ % solution. How much water is added to $15$ L of original solution?
6. A map uses scale $1:50,000$ . Two points are $7.2$ cm apart. What is the actual distance in km?
7. A machine's output is proportional to the square of its speed. If speed rises from $4$ to $6$ , output is multiplied by what factor?
8. A merchant sells an item for $84$ dollars at a $30\%$ profit on cost. What was the cost?
9. Three numbers are in ratio $2:3:5$ . If the largest exceeds the smallest by $42$ , find their sum.