## Ratio and Proportion Questions for SSC/RRB Exams (05 – 04 – 2018)

Ratio and Proportion Questions for SSC/RRB Exams (05 – 04 – 2018)
1. Find the ratio of b : a given that 0.2a + 0.3b = 0.4 and 0.3a + 0.4b = 0.6
a) 2
b) 0
c) -2
d) Can’t be determined
Solution:
Multiplying the equations as follows:
0.2a + 0.3b = 0.4   -----(1) × 3
0.3a + 0.4b = 0.6   -----(2) × 2
0.6a + 0.9b = 1.2
And, 0.6a + 0.8b = 1.2
Subtracting the above 2 equations, we get: b = 0
Substituting the value of b in any of the equations, we get: a = 2
b : a = 0
2. Two numbers are in the ratio 3 : 4. If 4 be added to both of them, then their ratio becomes 5 : 6. Find the sum of the numbers:
a) 14
b) 15
c) 20
d) 25
Solution:
Given, two numbers are in the ratio 3 : 4.
Let the numbers be 3a and 4a respectively.
Given, if 4 be added to both of them, then their ratio becomes 5 : 6.
(3a + 4)/(4a + 4) = 5/6
18a + 24 = 20a + 20
2a = 4
a = 2
Sum of numbers = 3a + 4a = 7a = 14
3. In a school, the ratio of boys to girls is 5 : 4 and the ratio of girls to teachers is 8 : 1. The ratio of students to teachers is:
a) 18 : 1
b) 10 : 1
c) 8 : 3
d) 42 : 4
Solution:
Let the number of teachers be x.
ratio of girls : teachers = 8 : 1,
Number of girls = (8/1) × x = 8x
Now, since ratio of boys : girls = 5 : 4
Number of boys = (5/4) × 8x = 10x
Number of students = number of boys + number of girls = 10x + 8x = 18x
Ratio of student: teachers = 18x : x = 18 : 1
Hence, the ratio of students and teachers is 18: 1

4. In an ornament the ratio of silver and aluminium is 7 : 5. The percentage of aluminium in the ornament is:
a) 58 1/3
b) 41 2/3
c) 42.5
d) 57.5
Solution:
The percentage of aluminium in the ornament = 5/12 * 100 = 41 2/3
5. The number of students of a class is 66. The ratio of the number of male students to the number of female students is 5 : 6. The number of female students is
a) 18
b) 36
c) 30
b) 24
Solution:
Let the number of male and female students be 5x and 6x respectively.
Total number of students = 66
5x + 6x = 66
x = 6
number of females = 6x = 6 × 6 = 36
6. The present ages of three persons are in proportions 3: 7: 8. Six years ago, the sum of their ages was 36. Find their present ages (in years).
a) 8, 20, 28
b) 9, 21, 24
c) 20, 35, 45
d) Can’t be determined
Solution:
Let the present ages of persons be 3x, 7x and 8x respectively.
Six years ago,
Their ages would be (3x – 6), (7x – 6) and (8x – 6) years respectively.
Given: the sum of their ages was 36
Thus, (3x – 6) + (7x – 6) + (8x – 6) = 36
18x 18 = 36
18x = 54
x = 3
Therefore, their present years will be (3 × 3), (7 × 3) and (8 × 3) i.e., 9, 21 and 24 years respectively.
7. The ratio of third proportional to 12 and 30 and the mean proportional between 9 and 25 would be –
a) 3 : 4
b) 5 : 1
c) 2 : 7
d) 1 : 3
Solution: Let the third proportional to 12 and 30 be x
Then,12 : 30 : : 30 : x
12x = 30 * 30 x = 30*30/12 = 75
Third proportional to 12 and 30 = 75
Mean proportional between 9 and 25 = √9 * 25 = 15
Required ratio = 75 : 15
Required ratio = 5 :1
8. The fourth proportional to 0.12, 0.24, 8 is
a) 8.9
b) 56
c) 16
d) 17
Solution:
Mathematically the question can be written as,
0.12: 0.24 8: x [Where x = the fourth proportional]
0.12/0.24 = 8/x
½ = 8/x
x = 16

9. The fourth proportional to 75, 192 and 200 is equal to fourth proportional to 90, 384 and Q. Find the value of Q.
a) 100
b) 108
c) 120
d) 126
Solution:
Fourth proportional to 75, 192 and 200 will be R, if
75/192 = 200/R
R = (200 × 192)/75
Fourth proportional to 90, 384 and Q will be R, if
90/384 = Q/R
R = (384Q/90)
(384Q/90) = (200 × 192)/75
Q = (100 × 90)/75 = 120
10. The angles in a quadrilateral PQRS are such that angle S is fourth proportional of angles P, Q and R. If the ratio of angles Q and P is 5 : 4, and angle S is 125°, find the measure of angle R.
a) 90°
b) 100°
c) 108°
d) 120°