Ratio and proportion problems made easy

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment jobs. 1. Two numbers are in the ratio 7 : 11. If 7 is added to each of the […]

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment jobs.

1. Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. The smaller number is?
a) 29 b) 39 c) 49 d) 59
Ans: c
Solution: Let the numbers be 7x and 11x respectively.
 (7x 7) / (11x 7) = 2/3
 22x 14 = 21x 21
=>; x = 7
 Smaller number
= 7x = 7 × 7 = 49

2. The ratio between two numbers is 2 : 3. If each number is increased by 4, the ratio between them becomes 5 : 7. The difference between the numbers is?
a) 8 n) 10 c) 12 d) 14
Ans: a
Solution: Let the numbers be 2x and 3x.
 (2x 4) / (3x 4) = 5/7
 15x 20 = 14x 28
Required difference
=>; x = 28 – 20 = 8

3. Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5:7. The smaller number is?
a) 38 b) 15 c) 11 d) 23
Ans: b
Solution: Let the numbers be 3x and 5x.
 (3x 10) / (5x 10) = 5/7
=>; 25x 50 = 21x 70
=>; 4x = 20
=>; x = 5
 Smaller number = 3x
= 3 × 5 = 15

4. Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The larger number is?
a) 44 b) 35 c) 25 d) 56
Ans: d
Solution : Let the numbers be 4x and 7x.
 (4x 4) / (7x 4) = 3/5
=>; 21x 12 = 20x 20
=>; 21x – 20x = 20 – 12
=>; x = 8
 Larger number
= 7x = 7 × 8 = 56

5. What number should be added to or subtracted from each term of the ratio 17 : 24 so that it becomes equal to 1 : 2?
a) 7 is added b) 10 is subtracted c) 7 is subtracted d) 10 is added
Ans: b
Solution: Let the number x be added.
 (17 x) / (24 x) = 1/2
=>; 34 2x = 24 x
=>; 2x – x = 24 – 34
=>; x = –10
Hence, 10 should be subtracted.

6. Students in three classes are in the ratio 4 : 6 : 9. If 12 students are increased in each class, the ratio changes to 7 : 9 : 12. Then the total number of students in the three classes before the increase is?
a) 46 b) 56 c) 76 d) 86
Ans: c
Solution: Let the original number of students be 4x , 6x and 9x.
 (4x 12) / (6x 12) = 7/9
=>; 42x 84 = 36x 108
=>; 42x – 36x = 108 – 84
=>; 6x = 24
=>; x = 4
 Required number of students
= 19x = 19 × 4 = 76

To be continued…
M Venkat
Director
MVK Publications
Dilsukhnagar
7671002120