Q. If the price of a book is increased by 10% and then decreased by 10%, what is the net change in price?
A.0%
B.1%
C.2%
D.3%
Solution
Let the original price be $100. After a 10% increase, the price becomes $110. After a 10% decrease, the price becomes $110 - $11 = $99. The net change is -1%, so the answer is 0%.
Q. If the principal amount is $2000 and the total amount after 3 years at a certain rate of simple interest is $2400, what is the rate of interest? (2000)
A.5%
B.6.67%
C.10%
D.12%
Solution
The interest earned is $400. Using SI = PRT, we have 400 = 2000 * R * 3. Solving for R gives R = 6.67%.
Q. In a certain mixture, the ratio of sugar to water is 1:4. If 2 liters of sugar is added to the mixture, what will be the new ratio of sugar to water?
A.1:3
B.1:4
C.1:5
D.1:6
Solution
Let the initial amount of sugar be x liters and water be 4x liters. After adding 2 liters of sugar, the new ratio becomes (x + 2) : 4x.
Q. In a certain mixture, the ratio of sugar to water is 1:4. If 2 liters of sugar is added, what will be the new ratio if the total volume of the mixture is 10 liters?
A.1:3
B.1:2
C.1:4
D.1:5
Solution
Initial sugar = 1 part, water = 4 parts. Total = 5 parts. New sugar = 2 liters, water = 8 liters. Ratio = 2:8 = 1:4.
Q. In a certain town, the ratio of the number of men to women is 3:2. If there are 120 men, how many women are there?
A.80
B.60
C.40
D.100
Solution
If the ratio of men to women is 3:2, then for every 3 men, there are 2 women. If there are 120 men, we can set up the proportion: 3/2 = 120/x. Solving for x gives x = 80. Therefore, there are 80 women.
Q. In a certain town, the ratio of the number of men to women is 3:4. If there are 120 men, how many women are there?
A.80
B.90
C.100
D.110
Solution
If the ratio of men to women is 3:4, then for every 3 men, there are 4 women. If there are 120 men, we can set up the proportion: 3/4 = 120/x. Cross-multiplying gives us 3x = 480, so x = 160. Therefore, there are 160 women.
Q. In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)
A.10
B.15
C.20
D.25
Solution
Let the number of boys be x and the number of girls be 30 - x. The total score of boys is 80x and that of girls is 70(30 - x). The overall average is given by (80x + 70(30 - x)) / 30 = 75. Solving this gives x = 15.
Q. In a mixture of two liquids, if the first liquid is 25% alcohol and the second is 75% alcohol, what is the overall percentage of alcohol if equal volumes of both liquids are mixed?
Q. In a mixture of two liquids, if the first liquid is 60% pure and the second is 80% pure, what is the overall purity if they are mixed in equal volumes?
Q. In a mixture of two types of tea, if the first type costs $5 per kg and the second type costs $7 per kg, what is the cost per kg of the mixture if they are mixed in the ratio 2:3?
Q. In a survey, the average age of a group of people is 30 years. If one person aged 40 leaves the group, what will be the new average age if the group originally had 10 people? (2023)
A.28
B.29
C.30
D.31
Solution
New total age = (30 × 10) - 40 = 260. New average = 260 / 9 = 28.89, which rounds to 29.
Q. In a survey, the average age of a group of people is 40 years. If one person aged 60 leaves the group, what will be the new average age if the group originally had 10 members? (2023)
A.38
B.39
C.40
D.41
Solution
Total age = 40 × 10 = 400. New total age = 400 - 60 = 340. New average = 340 / 9 = 37.78, which rounds to 38.
