__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

**Answer: B)**

**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

**Answer: A)**

**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

**Answer: A)**

**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

**Answer: B)**

**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

**Answer: B)**

**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

**Answer: B)**

**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

**Answer: B)**

**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

**Answer: C)**

**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

**Answer: C)**

**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°

**Answer: B)**

**Solution:**

Angle
S is fourth proportional of angles P, Q and R.

⇒ P/Q = R/S

Ratio
of angles Q and P is 5 : 4, and angle S is 125°.

So,
P/Q = 4/5

⇒ 4/5 =
R/125

⇒ R = 4 × 25 = 100

∴ Measure of
angle R is 100°.