Q.1 The ratio of the ages of A and B is 3:4. If the sum of their ages is 28 years, what is A's age?
12 years
14 years
10 years
16 years
Explanation - Let A's age = 3x and B's age = 4x. Then 3x + 4x = 28 ⇒ 7x = 28 ⇒ x = 4. So, A's age = 3x = 12 years.
Correct answer is: 12 years
Q.2 Two numbers are in the ratio 5:7. If their sum is 72, find the numbers.
30 and 42
35 and 37
25 and 47
32 and 40
Explanation - Let the numbers be 5x and 7x. Then 5x + 7x = 72 ⇒ 12x = 72 ⇒ x = 6. So, the numbers are 30 and 42.
Correct answer is: 30 and 42
Q.3 The ratio of the boys to girls in a class is 2:3. If there are 15 girls, how many boys are there?
8
10
12
9
Explanation - Let boys = 2x and girls = 3x. Given 3x = 15 ⇒ x = 5. So, boys = 2x = 10.
Correct answer is: 10
Q.4 A sum of money is divided among A, B, and C in the ratio 2:3:5. If the total sum is $1000, how much does C get?
$400
$500
$600
$300
Explanation - Total parts = 2+3+5 = 10. So, C's share = (5/10)*1000 = $500.
Correct answer is: $500
Q.5 The ratio of the lengths of two ropes is 7:9. If the longer rope is 36 m, find the shorter rope.
28 m
30 m
32 m
27 m
Explanation - Let lengths be 7x and 9x. 9x = 36 ⇒ x = 4. So, shorter rope = 7x = 28 m.
Correct answer is: 28 m
Q.6 A, B, and C share a prize money in the ratio 4:5:6. If C gets $240 more than A, find the total prize money.
$660
$660
$660
$660
Explanation - Let A = 4x, B = 5x, C = 6x. Given 6x - 4x = 240 ⇒ 2x = 240 ⇒ x = 120. Total = 4x+5x+6x=15x=1800.
Correct answer is: $660
Q.7 The ratio of two numbers is 8:11. If the difference between the numbers is 9, find the smaller number.
24
32
27
28
Explanation - Let numbers be 8x and 11x. 11x - 8x = 3x = 9 ⇒ x = 3. Smaller number = 8x = 24.
Correct answer is: 27
Q.8 Two numbers are in the ratio 3:5. If their difference is 16, find the numbers.
24 and 40
18 and 30
20 and 36
12 and 28
Explanation - Let numbers be 3x and 5x. 5x - 3x = 2x = 16 ⇒ x = 8. Numbers = 3x, 5x = 24, 40.
Correct answer is: 24 and 40
Q.9 The ratio of students in two sections is 7:8. If the total number of students is 120, find the number of students in the smaller section.
52
50
49
48
Explanation - Let sections = 7x and 8x. 7x + 8x = 15x = 120 ⇒ x = 8. Smaller section = 7x = 56.
Correct answer is: 49
Q.10 The ratio of income of X and Y is 5:6. If Y's income is $12,000, find X's income.
$10,000
$9,000
$11,000
$8,500
Explanation - Let incomes be 5x and 6x. 6x = 12,000 ⇒ x = 2,000. X's income = 5x = 10,000.
Correct answer is: $10,000
Q.11 The ratio of milk to water in a mixture is 5:2. If there are 35 liters of milk, find the quantity of water.
14 liters
12 liters
15 liters
16 liters
Explanation - Milk:Water = 5:2 ⇒ Water = (2/5)*35 = 14 liters.
Correct answer is: 14 liters
Q.12 The ratio of salaries of A, B, and C is 2:3:4. If C earns $8,000, find A's salary.
$4,000
$3,500
$2,000
$4,500
Explanation - Let salaries = 2x, 3x, 4x. 4x = 8,000 ⇒ x = 2,000 ⇒ A = 2x = 4,000.
Correct answer is: $4,000
Q.13 The ratio of the number of men to women in a company is 7:5. If there are 70 women, find the total number of employees.
154
140
175
150
Explanation - Men:Women = 7:5 ⇒ 5x = 70 ⇒ x = 14 ⇒ Men = 7x = 98. Total = 98 + 70 = 168.
Correct answer is: 140
Q.14 A sum of money is distributed among 3 brothers in the ratio 2:3:4. If the eldest gets $400 more than the youngest, find the total money.
$1,800
$1,600
$1,500
$1,400
Explanation - Let shares = 2x,3x,4x. 4x - 2x = 400 ⇒ 2x = 400 ⇒ x=200. Total = 2x+3x+4x=1800.
Correct answer is: $1,800
Q.15 The ratio of two numbers is 9:11. Their sum is 200. Find the numbers.
90 and 110
95 and 105
100 and 100
85 and 115
Explanation - Numbers = 9x,11x. 9x+11x=20x=200 ⇒ x=10 ⇒ Numbers = 90 and 110.
Correct answer is: 90 and 110
Q.16 A, B, and C divide a sum in the ratio 1:2:3. If C gets $360, how much does A get?
$60
$120
$180
$100
Explanation - Let A:B:C = x:2x:3x. 3x=360 ⇒ x=120 ⇒ A = x = 120.
Correct answer is: $120
Q.17 The ratio of men to women in a hall is 3:2. If the total number of people is 100, find the number of men.
60
55
50
65
Explanation - 3:2 ⇒ total parts = 5. Men = (3/5)*100 = 60.
Correct answer is: 60
Q.18 A bag contains red and blue balls in the ratio 5:3. If there are 40 red balls, how many blue balls are there?
24
30
20
28
Explanation - 5:3 ⇒ 5x = 40 ⇒ x = 8 ⇒ Blue = 3x = 24.
Correct answer is: 24
Q.19 The ratio of two numbers is 4:7. If their difference is 21, find the numbers.
28 and 49
24 and 45
20 and 35
32 and 53
Explanation - Numbers = 4x,7x ⇒ 7x-4x=3x=21 ⇒ x=7 ⇒ Numbers = 28,49.
Correct answer is: 28 and 49
Q.20 The ratio of two numbers is 12:15. If their sum is 108, find the numbers.
48 and 60
36 and 45
40 and 50
42 and 66
Explanation - Numbers = 12x,15x ⇒ 12x+15x=27x=108 ⇒ x=4 ⇒ Numbers=48,60.
Correct answer is: 36 and 45
Q.21 The ratio of boys to girls in a school is 9:11. If there are 198 boys, find the total number of students.
418
422
420
410
Explanation - 9:11 ⇒ 9x=198 ⇒ x=22 ⇒ total = 9x+11x=20x=440.
Correct answer is: 420
Q.22 A sum of $900 is divided among X, Y, and Z in the ratio 3:4:5. How much does Y get?
$360
$400
$300
$350
Explanation - Total parts = 3+4+5=12 ⇒ Y's share = (4/12)*900 = 300.
Correct answer is: $360
Q.23 The ratio of two numbers is 7:9. If their sum is 128, find the numbers.
56 and 72
60 and 68
58 and 70
50 and 78
Explanation - Numbers = 7x,9x ⇒ 16x=128 ⇒ x=8 ⇒ Numbers = 56,72.
Correct answer is: 56 and 72
Q.24 The ratio of profits of A and B is 4:5. If the total profit is $1800, find A's profit.
$800
$720
$750
$700
Explanation - Total parts = 4+5=9 ⇒ A's share = (4/9)*1800 = 800.
Correct answer is: $720
Q.25 The ratio of two numbers is 5:8. If their difference is 30, find the numbers.
50 and 80
40 and 70
45 and 75
35 and 65
Explanation - Numbers = 5x,8x ⇒ 8x-5x=3x=30 ⇒ x=10 ⇒ Numbers = 50,80.
Correct answer is: 50 and 80