We have already covered the concepts of ratio and proportion and practiced them through exercises and practice tests. Now it is time to solve actual previous year questions (PYQs) asked in SSC, RRB, Banking, Defence, and other competitive examinations.
Each question is provided with a detailed solution. However, students are strongly advised to attempt the questions on their own before looking at the answers. This will help strengthen their concepts and improve their problem-solving skills.
If you want to revise the basics, you can visit our Ratio and Proportion page and Ratio Formula with Examples and Explanations page. You can also attempt our Ratio and Proportion Practice Questions with Answers section for additional practice.
Question 1:
If 15% of x is equal to 25% of y, then find x : y.
A. 5 : 3 B. 3 : 5 C. 2 : 3 D. 4 : 5
Solution:
Given,
15% of x = 25% of y
Converting percentages into fractions:
15/100 × x = 25/100 × y
Cancelling 100 from both sides:
15x = 25y
Dividing both sides by 5:
3x = 5y
Therefore,
x/y = 5/3
Hence,
x : y = 5 : 3
Answer: A. 5 : 3
SSC/RRB/Defence/Banking Shortcut
Whenever you have:
a% of X = b% of Y
Then,
X : Y = b : a
Therefore,
x : y = 25 : 15
= 5 : 3
Answer = 5 : 3
Question 2:
If 9 : x = 22.5 : 27, then find the value of x.
A. 9.6 B. 10.8 C. 11.2 D. 12
Solution:
Given,
9 : x = 22.5 : 27
Using the property of proportion,
9/x = 22.5/27
Cross-multiplying,
9 × 27 = 22.5 × x
243 = 22.5x
Therefore,
x = 243 ÷ 22.5
x = 10.8
Hence,
x = 10.8
Answer: B. 10.8
Question 3:
If 40% of A = 0.2 of B = 1/4 of C, then find A : B : C.
A. 5 : 10 : 8 B. 5 : 8 : 10 C. 8 : 10 : 5 D. 10 : 8 : 5
Solution:
Given,
40% of A = 0.2 of B = 1/4 of C
Let the common value be k.
Then,
40% of A = k
40/100 × A = k
2/5 × A = k
A = 5k/2
Also,
0.2 × B = k
1/5 × B = k
B = 5k
And,
1/4 × C = k
C = 4k
Therefore,
A : B : C = 5k/2 : 5k : 4k
Multiplying each term by 2 to remove the denominator,
A : B : C = 5 : 10 : 8
Hence,
A : B : C = 5 : 10 : 8
Answer: A. 5 : 10 : 8
SSC/RRB/Defence/Banking Shortcut
When
40% of A = 20% of B = 25% of C
the ratio is inversely proportional to the percentages.
A : B : C = 1/40 : 1/20 : 1/25
Taking LCM 100:
A : B : C = 100/40 : 100/20 : 100/25
= 2.5 : 5 : 4
Multiplying by 2:
= 5 : 10 : 8
Question 4:
If p : q = 5 : 3, then find the ratio (3p + 4q) : (3p – 2q).
A. 9 : 3 B. 27 : 9 C. 27 : 11 D. 11 : 27
Solution:
Given,
p : q = 5 : 3
Let,
p = 5x
q = 3x
Substituting the values in the given expression,
(3p + 4q) : (3p – 2q)
= [3(5x) + 4(3x)] : [3(5x) – 2(3x)]
= (15x + 12x) : (15x – 6x)
= 27x : 9x
Cancelling x from both terms,
= 27 : 9
Therefore,
(3p + 4q) : (3p – 2q) = 27 : 9
Answer: B. 27 : 9
Use the ratio values directly:
p = 5
q = 3
Then,
(3×5 + 4×3) : (3×5 – 2×3)
= (15 + 12) : (15 – 6)
= 27 : 9
Answer = 27 : 9
Question 5:
At a coaching institute, the ratio of students preparing for SSC CGL and RRB NTPC is 13 : 12. What percentage of the students are preparing for SSC CGL?
A. 48% B. 50% C. 52% D. 54%
Solution:
Given,
SSC CGL : RRB NTPC = 13 : 12
We know the formula: Formula to Divide a Quantity in a Given Ratio
If a quantity Q is divided in the ratio A : B, then
First Share = [A/(A + B)] × Q
Second Share = [B/(A + B)] × Q
Since we need the percentage of SSC CGL students, let the total number of students be 100.
Using the formula:
SSC CGL Students
= [13/(13 + 12)] × 100
= (13/25) × 100
= 52
Therefore,
Percentage of SSC CGL Students = 52%
Answer: C. 52%
SSC Shortcut
Percentage of SSC CGL Students
= [13/(13 + 12)] × 100
= (13/25) × 100
= 52%
Answer = 52%
Question 6:
What must be added to each term of the ratio 8 : 14 so that it becomes equal to 3 : 4?
A. 2 B. 3 C. 4 D. 10
Solution:
Let x be added to each term.
Then,
(8 + x) : (14 + x) = 3 : 4
Using the property of proportion,
(8 + x)/(14 + x) = 3/4
Cross-multiplying,
4(8 + x) = 3(14 + x)
32 + 4x = 42 + 3x
4x – 3x = 42 – 32
x = 10
Therefore,
10 must be added to each term.
Verification:
(8 + 10) : (14 + 10)
= 18 : 24
= 3 : 4
Hence,
Required number = 10
Question 7:
If 60% of A = 1/4 of B, then A : B is:
A. 5 : 12 B. 5 : 6 C. 12 : 5 D. 6 : 5
Solution:
Given,
60% of A = 1/4 of B
Converting 60% into a fraction:
60/100 × A = 1/4 × B
3/5 × A = 1/4 × B
Cross-multiplying,
12A = 5B
Therefore,
A/B = 5/12
Hence,
A : B = 5 : 12
Answer: A. 5 : 12
Question 8:
Which of the following represents xy = 100?
A. 20 : x = y : 5
B. x : 25 = y : 5
C. x : 10 = y : 10
D. 40 : x = y : 2
Solution:
We know that:
xy = 100
Let us check each option using the property of proportion:
First × Fourth = Second × Third
Option A
20 : x = y : 5
Cross-multiplying,
20 × 5 = xy
100 = xy
xy = 100
This matches the given condition.
Option B
x : 25 = y : 5
Cross-multiplying,
5x = 25y
x = 5y
This does not represent xy = 100.
Option C
x : 10 = y : 10
Cross-multiplying,
10x = 10y
x = y
This does not represent xy = 100.
Option D
40 : x = y : 2
Cross-multiplying,
40 × 2 = xy
80 = xy
xy = 80
This also does not represent the given condition.
Question 9:
Which of the following is the lowest ratio?
A. 9 : 20 B. 17 : 28 C. 13 : 18 D. 25 : 36
Solution:
To find the lowest ratio, convert each ratio into a fraction and compare their values.
Option A
9 : 20 = 9/20 = 0.45
Option B
17 : 28 = 17/28 = 0.607
Option C
13 : 18 = 13/18 = 0.722
Option D
25 : 36 = 25/36 = 0.694
Comparing the values:
9/20 = 0.45
17/28 ≈ 0.607
25/36 ≈ 0.694
13/18 ≈ 0.722
The smallest value is:
9/20
Therefore,
The lowest ratio is 9 : 20.
Answer: A. 9 : 20
Question 10:
If the ratio of students preparing for SSC CGL and SSC CHSL is 2 : 3, and the ratio of SSC CGL and RRB NTPC aspirants is 1 : 2, then what is the ratio of SSC CHSL aspirants to RRB NTPC aspirants?
A. 2 : 3 B. 3 : 4 C. 3 : 5 D. 3 : 6
Solution:
Given,
SSC CGL : SSC CHSL = 2 : 3
and
SSC CGL : RRB NTPC = 1 : 2
Since SSC CGL is common in both ratios, make its value equal.
Multiply the second ratio by 2:
SSC CGL : RRB NTPC
= 1 : 2
= 2 : 4
Now,
SSC CGL : SSC CHSL = 2 : 3
SSC CGL : RRB NTPC = 2 : 4
Combining the two ratios:
SSC CGL : SSC CHSL : RRB NTPC
= 2 : 3 : 4
Therefore,
SSC CHSL : RRB NTPC
= 3 : 4
Answer: B. 3 : 4
Question 11:
If p:q:r=2:3:4 and 3p−q+2r=39 then find the value of r.
A. 8.2 B. 12.5 C. 14.18 D. 20.3
Solution:
Given,
p : q : r = 2 : 3 : 4
Let,
p = 2x
q = 3x
r = 4x
Substituting these values into the given equation:
3p − q + 2r = 39
3(2x) − 3x + 2(4x) = 39
6x − 3x + 8x = 39
11x = 39
x = 39/11
Now,
r = 4x
r = 4 × 39/11
r = 156/11
r = 14.18
Answer: C, 14.18.
Question 12:
If p:q:r=1:2:4 then p^2:q^2:r^2 is equal to:
A. 1 : 2 : 4 B. 1 : 4 : 16 C. 1 : 8 : 64 D. 2 : 4 : 8
Solution:
Given,
p : q : r = 1 : 2 : 4
Squaring each term of the ratio:
p² : q² : r²
= 1² : 2² : 4²
= 1 : 4 : 16
Therefore,
p² : q² : r² = 1 : 4 : 16
Answer: B. 1 : 4 : 16
SSC/RRB/Defence/Banking Shortcut
1 : 2 : 4
Square each term:
1² : 2² : 4²
= 1 : 4 : 16
Question 13:
If p : q = q : r, then p⁴ : q⁴ is equal to:
A. pr : q²
B. p² : r²
C. r² : p²
D. q² : pr
Solution:
Given,
p : q = q : r
Using the property of proportion,
p × r = q × q
pr = q²
Now,
p⁴ : q⁴
can be written as:
(p²)² : (q²)²
Using
q² = pr
we get:
p⁴ : q⁴
= p² × p² : q² × q²
Dividing both terms by p2q2
= p²/q² : q²/p²
Since
q² = pr
= p² : r²
Therefore,
p⁴ : q⁴ = p² : r²
Answer: B. p² : r²
SSC/RRB/Defence/Banking Shortcut
Given,
p : q = q : r
Therefore,
q² = pr
Now,
p⁴ : q⁴
= (p²)² : (q²)²
= p² : r²
Question 14:
If the ratio of students preparing for SSC CGL to the total number of students preparing for RRB NTPC and Banking is 1 : 3, and the ratio of Banking aspirants to the total number of SSC CGL and RRB NTPC aspirants is 5 : 7, then the ratio of RRB NTPC aspirants to the total number of SSC CGL and Banking aspirants is:
A. 1 : 2
B. 2 : 3
C. 1 : 3
D. 2 : 1
Solution:
Let:
SSC CGL = S
RRB NTPC = R
Banking = B
Given,
S : (R + B) = 1 : 3
Therefore,
R + B = 3S
Also,
B : (S + R) = 5 : 7
Therefore,
7B = 5(S + R)
Substituting
R = 3S − B
into the second equation:
7B = 5[S + (3S − B)]
7B = 5(4S − B)
7B = 20S − 5B
12B = 20S
3B = 5S
B : S = 5 : 3
Let,
S = 3x
B = 5x
Using
R + B = 3S
R + 5x = 9x
R = 4x
Therefore,
S : R : B = 3 : 4 : 5
Required ratio:
R : (S + B)
= 4 : (3 + 5)
= 4 : 8
= 1 : 2
Answer: A. 1 : 2
Question 15:
At a coaching institute, 15% of the students preparing for SSC CGL is equal to 40% of the students preparing for RRB NTPC. What is the ratio of SSC CGL aspirants to RRB NTPC aspirants?
A. 8 : 3
B. 3 : 8
C. 5 : 2
D. 2 : 5
Solution:
Given,
15% of SSC CGL Aspirants = 40% of RRB NTPC Aspirants
Let,
SSC CGL Aspirants = S
RRB NTPC Aspirants = R
Then,
15% of S = 40% of R
Converting percentages into fractions:
15/100 × S = 40/100 × R
Cancelling 100 from both sides:
15S = 40R
Dividing both sides by 5:
3S = 8R
Therefore,
S/R = 8/3
Hence,
SSC CGL : RRB NTPC = 8 : 3
Answer: A. 8 : 3
Question 16:
The fare of a local passenger train and an express train from Lucknow to Kanpur was ₹20 and ₹30 respectively. The express train fare was increased by 20% and the local passenger train fare was increased by 10%. What is the ratio of the new express train fare to the new local passenger train fare?
A. 3 : 5
B. 5 : 3
C. 11 : 18
D. 18 : 11
Solution:
Given,
Local Passenger Train Fare = ₹20
Express Train Fare = ₹30
Step 1: Find the New Express Train Fare
Increase = 20%
New Express Fare
= 30 + 20% of 30
= 30 + 6
= ₹36
Step 2: Find the New Local Passenger Train Fare
Increase = 10%
New Local Fare
= 20 + 10% of 20
= 20 + 2
= ₹22
Step 3: Find the Required Ratio
New Express Fare : New Local Fare
= 36 : 22
Dividing both terms by 2:
= 18 : 11
Therefore,
Required Ratio = 18 : 11
Answer: D. 18 : 11
Question 17:
A railway maintenance contract worth ₹53 lakh is shared among three contractors A, B and C. Contractor A receives ₹7 lakh more than Contractor B, and Contractor B receives ₹8 lakh more than Contractor C. What is the ratio of the amounts received by A, B and C?
A. 15 : 8 : 30
B. 16 : 9 : 18
C. 18 : 25 : 10
D. 25 : 18 : 10
Solution:
Given,
A = B + 7
B = C + 8
Let the amount received by C be x lakh.
Then,
C = x
B = x + 8
A = x + 15
The total contract value is ₹53 lakh.
Therefore,
(x + 15) + (x + 8) + x = 53
3x + 23 = 53
3x = 30
x = 10
Thus,
C = 10 lakh
B = 18 lakh
A = 25 lakh
Therefore,
A : B : C
= 25 : 18 : 10
Answer: D. 25 : 18 : 10
SSC/RRB/Defence/Banking Shortcut
Let C = x.
B = x + 8
A = x + 15
Using total = 53:
x + (x + 8) + (x + 15) = 53
3x + 23 = 53
x = 10
Hence,
A : B : C
= 25 : 18 : 10
Question 18:
In a recruitment drive, 2010 candidates were selected for the posts of ASO (Assistant Section Officer), Income Tax Inspector, and Examiner.
The selection ratio was such that:
- For every 5 ASO candidates selected, 12 Income Tax Inspectors were selected.
- For every 4 Income Tax Inspectors selected, 5.5 Examiners were selected.
By how many does the number of Examiner selections exceed the number of Income Tax Inspector selections?
A. 270
B. 360
C. 430
D. 620
Solution:
Given
ASO : Income Tax Inspector = 5 : 12
Income Tax Inspector : Examiner = 4 : 5.5
First remove the decimal:
Income Tax Inspector : Examiner
= 4 : 5.5
= 8 : 11
Now we have:
ASO : Income Tax Inspector = 5 : 12
Income Tax Inspector : Examiner = 8 : 11
Make Income Tax Inspector common.
LCM of 12 and 8 = 24
Multiply first ratio by 2:
ASO : Income Tax Inspector
= 10 : 24
Multiply second ratio by 3:
Income Tax Inspector : Examiner
= 24 : 33
Therefore,
ASO : Income Tax Inspector : Examiner
= 10 : 24 : 33
Total parts:
10 + 24 + 33 = 67
Total selected candidates:
67 parts = 2010
One part:
2010 ÷ 67 = 30
Therefore,
ASO = 10 × 30 = 300
Income Tax Inspector = 24 × 30 = 720
Examiner = 33 × 30 = 990
Difference:
990 − 720 = 270
Answer: A. 270
Question 19:
The ratio of the monthly salary and monthly expenditure of a Loco Pilot is 11 : 10. If the Loco Pilot saves ₹9,000 per year, what is his monthly salary?
A. ₹8,000
B. ₹8,250
C. ₹8,500
D. ₹8,800
Solution:
Given,
Salary : Expenditure = 11 : 10
Annual Savings:
₹9,000
Monthly Savings:
= 9000 ÷ 12
= ₹750
Let the salary and expenditure be:
11x and 10x
Therefore,
Savings = 11x − 10x
= x
But monthly savings are ₹750.
Hence,
x = 750
Monthly Salary:
= 11x
= 11 × 750
= ₹8,250
Therefore,
Monthly Salary = ₹8,250
Answer: B. ₹8,250
SSC/RRB/Defence/Banking Shortcut
Salary : Expenditure = 11 : 10
Difference:
11 − 10 = 1
Monthly Saving:
9000 ÷ 12 = ₹750
Therefore,
1 part = ₹750
Salary:
11 parts = 11 × 750
= ₹8,250
Question 20:
A refreshment stall at a railway station prepares 80 litres of milk tea mixture in which the ratio of milk to water is 7 : 3. To make the ratio of milk to water equal to 2 : 1, how many litres of water should be added to the mixture?
A. 4
B. 5
C. 6
D. 8
Solution
Given,
Milk : Water = 7 : 3
Total Mixture = 80 litres
Total parts:
7 + 3 = 10
Milk:
= (7/10) × 80
= 56 litres
Water:
= (3/10) × 80
= 24 litres
Let x litres of water be added.
Then,
Milk = 56 litres
Water = (24 + x) litres
New ratio:
56 : (24 + x) = 2 : 1
Cross-multiplying,
56 = 2(24 + x)
56 = 48 + 2x
2x = 8
x = 4
Therefore,
Water to be added = 4 litres
Answer: A. 4 litres
Question 21:
The monthly salaries of two employees working in a bank are in the ratio 8 : 9. If the salary of Employee A is increased by 50% and the salary of Employee B is reduced by 25%, the new ratio of their salaries becomes 16 : 9. What is the monthly salary of Employee A?
A. ₹22,000
B. ₹28,500
C. ₹37,000
D. Cannot be determined
E. None of these
Solution:
Given:
A : B = 8 : 9
Let
A = 8x
B = 9x
After changes:
A increases by 50%
New A = 8x × 150/100
= 12x
B decreases by 25%
New B = 9x × 75/100
= 27x/4
Therefore,
New Ratio
= 12x : 27x/4
Multiplying both terms by 4:
= 48x : 27x
= 16 : 9
The given new ratio is exactly:
16 : 9
which is true for every value of x. But from this, we can’t find out the salary of employees.
Answer: D. Cannot be determined
Question 22:
The number of workers assigned to a railway track maintenance project and the number of days required to complete the project vary inversely. When 12 workers are assigned, the work is completed in 9 days. Which of the following is not a possible combination of workers and days required?
A. 9 workers and 12 days
B. 18 workers and 6 days
C. 24 workers and 18 days
D. 36 workers and 3 days
Solution
Since the number of workers and the number of days vary inversely,
we use the formula:
Workers × Days = Constant
Initially,
12 × 9 = 108
Now check each option.
Option A
9 × 12 = 108
Possible.
Option B
18 × 6 = 108
Possible.
Option C
24 × 18 = 432
This is not equal to 108.
Therefore, this combination is not possible.
Option D
36 × 3 = 108
Possible.
Hence,
The incorrect combination is 24 workers and 18 days.
Answer: C. 24 workers and 18 days
Question 23:
The ratio of students preparing for SSC CGL to students preparing for RRB NTPC at a coaching institute is 3 : 1. What percentage of the students are preparing for SSC CGL?
A. 75%
B. 25%
C. 66⅔%
D. 33⅓%
Solution:
Given,
SSC CGL : RRB NTPC = 3 : 1
Total parts:
3 + 1 = 4
Using the formula:
Percentage of a Part
If two quantities are in the ratio A : B, then
Percentage of the First Quantity
= A / (A + B) × 100
Applying the formula,
Percentage of SSC CGL Students
= 3/(3 + 1) × 100
= 3/4 × 100
= 75%
Therefore,
Percentage of SSC CGL Students = 75%
Answer: A. 75%
SSC/RRB/Defence/Banking Shortcut
Ratio = 3 : 1
Total Parts = 4
SSC CGL Percentage
= (3/4) × 100
= 75%
Question 24:
Find the third proportional to 12 and 18.
A. 24
B. 27
C. 30
D. 36
Solution:
Find the third proportional to 12 and 18.
12 : 18 = 18 : x
Since 18 is the common term,
x = 18² ÷ 12
= 324 ÷ 12
= 27
Therefore,
The third proportion is 27.
Answer: B. 27
Question 25:
Find the fourth proportional to 8, 12 and 18.
A. 24
B. 27
C. 30
D. 36
Solution:
Let the fourth proportional be x.
Then,
8 : 12 = 18 : x
Converting the ratios into fractions,
8/12 = 18/x
Cross-multiplying,
8x = 12 × 18
x = (12 × 18)/8
= 216/8
= 27
Therefore,
The fourth proportion is 27.
Answer: B. 27
Question 26:
Find the mean proportional between 16 and 36.
A. 20
B. 22
C. 24
D. 26
Solution:
Let the mean proportional be x.
Then,
16 : x = x : 36
Converting the ratios into fractions,
16/x = x/36
Cross-multiplying,
x² = 16 × 36
x² = 576
Taking the square root of both sides,
x = √576
x = 24
Therefore,
The mean proportional is 24.
Answer: C. 24
SSC/RRB/Defence/Banking Shortcut
16 : x = x : 36
x² = 16 × 36
x = √(16 × 36)
= √576
= 24
Answer = C. 24
Question 27:
The monthly salaries of an Assistant Section Officer (ASO) and an Income Tax Inspector are in the ratio 5 : 4. The ASO spends 3/5 of his salary on household expenses, 15% on his child’s education, and 18% on loan repayments. The remaining amount is ₹2,100.
What is the monthly salary of the Income Tax Inspector?
A. ₹25,000
B. ₹30,000
C. ₹15,000
D. ₹24,000
Solution:
Let the monthly salary of the ASO be ₹x.
The ASO spends:
Household Expenses = 3/5 = 60%
Child’s Education = 15%
Loan Repayments = 18%
Total expenditure:
60% + 15% + 18%
= 93%
Therefore, the remaining savings are:
100% − 93%
= 7%
Given,
7% of ASO’s Salary = ₹2,100
So,
ASO’s Salary
= (2100 × 100)/7
= ₹30,000
Now,
ASO : Income Tax Inspector
= 5 : 4
Therefore,
Income Tax Inspector’s Salary
= (4/5) × 30,000
= ₹24,000
Answer: D. ₹24,000
Question 28:
Two friends start a business partnership. Amit invests ₹20,000 and Rohit invests ₹30,000. If the total profit at the end of the year is ₹25,000, what is Rohit’s share of the profit?
A. ₹10,000
B. ₹12,000
C. ₹15,000
D. ₹18,000
Solution:
Since both partners invest their money in the business in different amounts, the profit is divided in the ratio of their investments.
Investment ratio:
Amit : Rohit
= 20,000 : 30,000
= 2 : 3
Total ratio:
2 + 3 = 5
Rohit’s share of the profit:
= (3/5) × 25,000
= ₹15,000
Therefore,
Rohit’s Share = ₹15,000
Answer: C. ₹15,000
SSC/RRB/Defence/Banking Shortcut
Investment Ratio
= 20,000 : 30,000
= 2 : 3
Rohit’s share:
= (3/5) × 25,000
= ₹15,000
Answer = C. ₹15,000
FAQ:
1. Are ratio and proportion questions asked in SSC, RRB and Banking exams?
Yes. Ratio and proportion is one of the most important arithmetic chapters for competitive exams. Questions are regularly asked in:
- SSC CGL
- SSC CHSL
- SSC MTS
- SSC GD
- RRB NTPC
- RRB Group D
- RRB ALP
- RRB Technician
- Banking Exams
- Defence Exams
2. Which topics should I study after ratio and proportion?
After mastering ratio and proportion, students should study:
Percentage, Profit and Loss, Simple Interest & Compound Interest, Partnership, Mixture and Alligation, Time and Work, Time, Speed and Distance
These chapters heavily use ratio concepts.
In how many days we can have mastery over the Ratio and Proportion section?
If you learn all the formulas, practice all the questions and revise, you can get hold of it within 2-3 weeks.
Related Resources to Ratio and Proportion
- Ratio and Proportion
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- Ratio Word Problems with Answers
- Ratio Formula with Examples and Explanations
- Ratio and Proportion Practice Questions with Answers
- Inverse Proportion Questions & Answers with Solutions
- Direct Proportion Questions and Answers
- Unitary Method Questions and Answers with Solutions
- Proportion Questions and Answers with Solutions
- Profit, Loss & Discount PYQs SSC, RRB, Banking & Defence Exams (Solved)