1. A particular sum was divided among A, B and C in ratio 2:6:7 respectively. If the amount received by A was Rs. 4,908, what was the difference between the amounts received by B and C?
- Rs. 2,454
- Rs. 3,494
- Rs. 2,135
- Rs. 2,481
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Solution:
If the total amount be Rs. x, then (2x / 15) = 4908
x = (4908 × 15) / 2 = Rs. 36810
Required difference = [(7 – 6) / 15] × 36810 = Rs. 2454
2. The average age of a man and his son is 30 years. The ratio of their ages four years ago was 10:3 respectively. What is the difference between the present ages of the man and his son?
- 28 years
- 16 years
- 26 years
- 44 years
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3. The ratio between Gloria's and Sara's present ages is 4:7 respectively, Two years ago the ratio between their ages was 1:2 respectively. What will be Sara’s age three years hence?
- 17 years
- 14 years
- 11 years
- 8 years
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Solution:
Let Gloria’s and Sara's present ages be 4x and 7x years respectively
Two years ago, (4x – 2) / (7x – 2) = 1 / 2
8x – 4 = 7 x – 2 àx = 2
Sara’s age three years hence = 7x + 3 = 17 years
4. The total number of students in a school is 31700. If the ratio of boys to the girls in the school is 743:842 respectively, what is the total number of girls in the school?
- 14860
- 16480
- 15340
- None of these
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Solution:
Boys : Girls = 743 : 842
Total number of students = 31700
Number of girls = [842 / (743 +842)] × 31700 = (842 / 1585) × 31700
= 16840
5. The ratio of the ages of A and B seven years ago was 3:4 respectively. The ratio of their ages nine years from now will be 7:8 respectively. What is B’s age at present?
- 16 years
- 19 years
- 28 years
- 23 years
20
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Solution:
A's present age = (3x + 7) years
B’s present age = (4x + 7) years, After 9 years,
(3x + 7 + 9) / (4x + 7 + 9) = 7 / 8
(3x + 16) / (4x + 16) = 7 / 8à (3x + 16) / (x + 4) = 7 / 2
7x + 28 = 6x + 32à x = 32 – 28
x = 4, B’s present age = 4x + 7 = 23 years
6. The ratio of the ages of A and B is 4:3 respectively. The ratio of their ages eight years from now will be 6:5 respectively. How old was A, when B was 7 years old?
- 16 years
- 11 years
- 9 years
- 12 years
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Solution:
A's present age = 4x years, B’s present age = 3x years
After 8 years,
(4x + 8) / (3x + 8) = 6 / 5à 20x + 40 = 18x + 48
2x = 48 – 40 = 8
X = 4, B’s present age = 12 years
A’s age = 4x -5 = 16 – 5 = 11
10. he respective ratio between the present ages of father, mother and daughter is 7:6:2. The difference between mother's and the daughter’s age is 24 years. What is the father's age at present?
- 43 years
- 42 years
- 39 years
- 38 years
38
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View Answer
Solution:
According to the question,
6x – 2x = 24à4x = 24
X = 6
Father’s present age = 7x = 7×6 = 42 years
11. In a class of 60 students, where the girls are twice that of boys. Kamal ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is:
- 12
- 7
- 3
- 5
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Solution:
Girls : Boys = 2 : 1. Total no.of students is 60
Girls 60 × (2 / 3) = 40 and boys = 20.
Kamal has been ranked 17 which means there are 16 students before him of which 9 are girlsàremaining 7 are boys.
7 boys are ahead of Kamal + Kamal is the 8th boy, hence, there are (20 – 8) = 12 boys after him.
12. Two varieties of rice at Rs. 10 per kg and Rs. 12 per kg are mixed together in the ratio 1 : 2. What is the price of the resulting mixture?
- Rs. 10.50 per kg
- Rs. 10.67 per kg
- Rs. 11.20 per kg
- Rs. 11.33 per kg
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View Answer
Solution:
Let the amount of rice be 1 kg and 2 kg. (The given ratio is 1 : 2). So, total cost = 10 × 1 + 12 × 2 = 10 + 24 = 34
Rs. 34 is the cost of (1 + 2 = 3) kg of rice.
Cost per kg = (34 / 3) = 11.33 per kg
13. if A varies directly proportional to C, and B also varies directly proportional to C, which one of the following is not correct?
- (A + B) ∝ C
- (A – B) ∝ (1/C)
- √(AB) ∝ C
- (A / B) = constant
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Solution:
A ∝ C = A = K1C
B ∝ C = B = K2C
Where K1and K2 are constants
(A + B) = (K1 +K2)C
(K1 +K2) is again a constants
(A + B) ∝ C √(A.B) = √[ (K1C) × (K2C)] = √(K1 K2C)
Here √(K1 K2) is a constantà√(A . B)∝ C
(A / B) = (K1C / K2C) = (K1 / K2)
(K1/ K2) is (1/ K2) a constant
But, (A – B) = (K1C – K2C) = (K1 – K2) C
(K1– K2) is a constantà(A – B) ∝ C
14. If the ratio of the areas of two squares is 9 : 1, the ratio of their perimeters is:
- 9:1
- 3:1
- 3:4
- 1:3
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Solution:
(x2 / y2) = (9 / 1) where x and y are the sides of the two squares
= ratio of perimetersà(x /y) = (3 / 1)à(4x / 4y) = (12 / 4) = (3 / 1)
15. The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, then the percentage of the students who did not get scholarship is:
- 68%
- 78%
- 82%
- 72%
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Solution:
Number of students in school = 100 (let)
Boys = (3 / 5) × 100 = 60, Girls = 40
Students who did not get scholarship
Boys = 60 × (80 / 100) = 48
Girls = 40 × (75 / 100) = 30
Students who do not get scholarship = 78
Required percentage = 78
16. In a mixture of 60 litres, the ratio of acid and water is 2 : 1. If the ratio of acid and water is to be 1 : 2, then the amount of water (in litres) to be added to the mixture is
- 50
- 45
- 55
- 60
64
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View Answer
Solution:
In 60 litres of mixture,
Acid = (2/3) × 60 = 40 litres, Water = 20 litres
If x litres of water be mixed, then [40 / (20+ x)] = 1/2à 20 + x = 80
x = 80 – 20 = 60 litres
17. Salaries of Akash, Babloo and Chintu are in the ratio of 2 : 3 : 5. If their salaries were increased by 15%, 10% and 20% respectively, what will be the new ratio of their salaries?
- 3 : 3 : 10
- 23 : 33 : 60
- 20 : 22 : 40
- None of these
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Solution:
Required ratio = [(2 × 115) / 100] : [(3 × 110) / 100] : [(5 × 120) / 100]
230 : 330 : 600à23 : 33 : 60
18. If x : y = 3 : 4 then (7x + 3y) : (7x – 3y) is equal to :
- 5:2
- 4:3
- 11:3
- 3:1
71
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Solution:
(x / y) = (3 / 4)
(7x + 3y) / (7x – 3y) = [7 (x /y) + 3] / [7(x /y) – 3]
[7 × (3 / 4) + 3] / [7 × (3 / 4) – 3] = (21 + 12) / (21 – 12)
33 / 9 = 11 / 3 = 11 : 3
19. If A : B = 5 : 7 ; C : D = 2A : 3B then AC : BD is:
- 20:38
- 50:147
- 10:21
- None of these
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Solution:
(A / B) = (5 / 7)
(C / D) = (2 / 3) × (A / B) = (2 × 5) / (3 × 7) = (10 / 21)
(AC / BD) = (5 / 7) × (10 / 21) = 50 / 147
50 : 147
20. The ratio of weekly incomes of A and B is 9 : 7 and the ratio of their expenditures is 4 : 3. If each saves Rs. 200 per week, then the sum of their weekly incomes is
- Rs. 3,200
- Rs. 4,200
- Rs. 4,800
- Rs. 5,600
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