Q. A chemist has a solution that is 25% acid. How much of this solution must be mixed with 10 liters of a solution that is 50% acid to obtain a solution that is 40% acid?
A.5 liters
B.10 liters
C.15 liters
D.20 liters
Solution
Let x be the liters of 25% solution. The equation is 0.25x + 0.5(10) = 0.4(x + 10). Solving gives x = 15 liters.
Q. A customer buys a laptop for $800 after a discount of 20%. What was the marked price?
A.$1000
B.$900
C.$850
D.$800
Solution
Let the marked price be x. After a 20% discount, the selling price is 0.80x. Setting this equal to $800 gives 0.80x = $800, so x = $800 / 0.80 = $1000.
Q. A customer buys two items for $120 each. If the shopkeeper gives a discount of 10% on the total bill, what is the final amount paid by the customer? (2023)
A.$216
B.$220
C.$240
D.$250
Solution
Total cost before discount = 2 * $120 = $240. Discount = 10% of $240 = $24. Final amount = $240 - $24 = $216.
Q. A customer buys two items for $240 after a discount of 10% on each. What was the total marked price of the items?
A.$250
B.$260
C.$270
D.$280
Solution
Let the total marked price be x. After a 10% discount, the selling price is 0.90x. Setting this equal to $240 gives 0.90x = $240, so x = $240 / 0.90 = $266.67, which rounds to $280.
Q. A family has three children with ages 5, 10, and 15. If they have another child, what age must the new child be to maintain an average age of 10? (2023)
A.5
B.10
C.15
D.20
Solution
Current total age = 5 + 10 + 15 = 30. To maintain an average of 10 with 4 children, total age must be 40. Therefore, the new child's age must be 40 - 30 = 10.
Q. A fruit seller has apples and oranges in the ratio of 5:3. If he has 40 apples, how many oranges does he have?
A.24
B.30
C.32
D.36
Solution
If the ratio of apples to oranges is 5:3, then for every 5 apples, there are 3 oranges. If there are 40 apples, we can set up the proportion: 5/3 = 40/x. Cross-multiplying gives us 5x = 120, so x = 24. Therefore, there are 24 oranges.
Q. A group of friends went out for dinner. If the average cost per person was $20 and there were 5 people, what was the total cost of the dinner? (2023)
A.$80
B.$100
C.$120
D.$140
Solution
Total cost = Average cost per person × Number of people = 20 × 5 = $100.
Q. A mixture contains 40% alcohol and 60% water. If 5 liters of the mixture is taken out and replaced with 5 liters of pure alcohol, what will be the new percentage of alcohol in the mixture?
A.50%
B.55%
C.60%
D.65%
Solution
After removing 5 liters of the mixture, the remaining alcohol is 0.4 * (total volume - 5) + 5 liters of pure alcohol.
Q. A mixture contains 60% of liquid X and 40% of liquid Y. If 10 liters of liquid Y is added, what will be the new percentage of liquid X in the mixture if the total volume becomes 30 liters?
A.50%
B.40%
C.60%
D.70%
Solution
Initial volume of Y = 40% of 20 liters = 8 liters. New volume of Y = 8 + 10 = 18 liters. Volume of X = 30 - 18 = 12 liters. Percentage of X = (12/30) * 100 = 40%.
