Ratio and Proportion Questions 2022-23 | SSC/RAILWAY/BANK EXAMS

1. If ‘p’ is the mean proportional to ‘q’ and ‘r’. Then find the value of (q + p)4 ∶ (p + r)4?.

A. p4 ∶ r4.

B. r4 ∶ q4.

C. p4 ∶ q4.

D. r4 ∶ p4.

Correct Answer:- A. p4 ∶ r4
Explanation:-
Given in the question:
P is the mean proportion to ‘q’ and ‘r’.
Therefore:-
q/p = p/r
Concept:
By substituting the values of ‘p’ and ‘q’ in the given question we get;
q/p = p/r = k(let constant…)
⇒ q/p = k
⇒ q = pk ……..(1)
⇒ p/r = k
⇒ p = rk ………(2)
Putting the value of (1) and (2) in (q + p)4 ∶ (p + r)4
⇒ (pk + p)4 ∶ (rk + r)4
⇒ [p(k + 1)]4 ∶ [r(k + 1)]4
⇒ [p4(k + 1)4] ∶ [r4(k + 1)4]
⇒ p4 ∶ r4
∴ The value of (q + p)4 ∶ (p + r)4 is p4 ∶ r4

2. Four terms are in proportion. The first, second and fourth terms are 4, 22 and 33. Find the third term.

A. 12.

B. 9.

C. 6.

D. 16.

Correct Answer:- C. 6
Explanation:-
Fourth proportional: If 4 numbers a, b, c, and d are in proportion, then d = (b × c)/a
Let the numbers in proportion be 4, 22, c, and 33
⇒ (22 × c)/4 = 33
⇒ c = (4 × 33)/22
⇒ c = 6
∴ The third term is 6

3. If (x + 4), (x + 12), (x – 1), and (x + 5) are in proportion then the mean proportional between x and (x – 7)is:

x,y is quantity so the mean proportion = √ xy
⇒ √ 16 × √ 16 – 7
⇒ 4 × 3
⇒ 12
∴ 12 will be the mean proportion.

4. If third proportional of 3 and 12 be x and mean proportion of 16 and 4 is y, then x ∶ y is:

A. 3 : 2.

B. 6 : 1r

C. 3 : 8.

D.11 : 2.

Correct Answer:- B. 6 : 1
Explanation:-
Given
Third proportional to 3 and 12 be x
Mean proportion of 16 and 4 is y
Mean proportion of x and y = √xy
Third proportion of a and b = b2/a
Third proportional to 3 and 12 = (12 × 12)/3 = 48
Mean proportion of 16 and 4 = √(16 × 4) = 8
x ∶ y = 48 ∶ 8 = 6 ∶ 1
∴ The ratio of x and y is 6 ∶ 1.

5. Find the mean proportional between 60% of 10 and 50% of 108.

A. 18

B. 17

C. 16

D. 19

Correct Answer:- A. 18
Explanation:-
Given:
The given numbers are 60% of 10 and 50% of 108
Mean proportional between a and b = √(a × b)
First number = (60/100) × 10
⇒ 6
Second number = (50/100) × 108
⇒ 54
Mean proportional = √(6 × 54)
⇒ √(6 × 6 × 9)
⇒ √(6 × 6 × 3 × 3)
⇒ 6 × 3
⇒ 18
∴ The mean proportional between 60% of 10 and 50% of 108 is 18

Ratio and Proportion Questions 2022-23 | SSC/RAILWAY/BANK EXAMS

1. .When a sum of money was equally distributed among 49 children, each child received Rs. 20. If the same amount is equally distributed among children, such that each child gets Rs. 3.5, find the number of children..