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All questions of Ratio & Proportion for UPSC CSE Exam

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The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
  • a)
    20
  • b)
    30
  • c)
    48
  • d)
    58
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
**Given Information:**
- The sum of three numbers is 98.
- The ratio of the first number to the second number is 2:3.
- The ratio of the second number to the third number is 5:8.

**Let's solve the problem step by step:**

**Step 1:**
Let's assume the three numbers as follows:
- The first number = 2x
- The second number = 3x
- The third number = 8y

**Step 2:**
According to the given information, the sum of the three numbers is 98. Therefore, we can write the equation as:
2x + 3x + 8y = 98

**Step 3:**
Simplifying the equation, we get:
5x + 8y = 98

**Step 4:**
Now, we need to find the values of x and y in order to find the second number.

**Step 5:**
According to the given information, the ratio of the second number to the third number is 5:8. Therefore, we can write the equation as:
3x/8y = 5/8

**Step 6:**
Cross-multiplying the equation, we get:
24x = 40y

**Step 7:**
Simplifying the equation, we get:
3x = 5y

**Step 8:**
Now, we have two equations:
5x + 8y = 98
3x = 5y

**Step 9:**
Substituting the value of 3x from the second equation into the first equation, we get:
5(5y/3) + 8y = 98
25y/3 + 8y = 98
(25y + 24y)/3 = 98
49y/3 = 98
49y = 294
y = 294/49
y = 6

**Step 10:**
Substituting the value of y into the second equation, we get:
3x = 5(6)
3x = 30
x = 30/3
x = 10

**Step 11:**
Now, we can find the second number:
The second number = 3x = 3 * 10 = 30

Therefore, the correct answer is option **B) 30**.

An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?
  • a)
    67.5%
  • b)
    72.5%
  • c)
    77.5%
  • d)
    82.5%
Correct answer is 'B'. Can you explain this answer?

Sameer Rane answered
Say M and N are the total volumes of first and second alloys respectively.

Say C, Z and T represent Copper, Tin and Zinc percentages respectively in second alloy.

⇒ C + Z + T = 100 …… Eq.1

Amount of copper in the mixture = 0.90M + (C/100) x N = 0.85 x (M + N)

⇒ 0.05M = (0.85 – C/100) x N

⇒ C = 85 – 5 x (M/N) ….. Eq.2

Amount of Zinc in the mixture = 0.07M + (Z/100) x N = 0.05 x (M + N)

⇒ 0.02M = (0.05 – Z/100) x N

⇒ Z = 5 – 2 x (M/N) ….. Eq.3

Amount of copper in the mixture = 0.03M + (T/100) x N = 0.10 x (M + N)

⇒ –0.07M = (0.10 – T/100) x N

⇒ T = 10 + 7 x (M/N) …… Eq.4

Given Zinc percent in second alloy is Zero

⇒ Z = 0

Eq.3 ⇒ 0 = 5 – 2 x (M/N)

⇒ M/N = 5/2

Substitute M/N = 5/2 in Eq.4

⇒ T = 10 + 7 x (5/2) = 10 + 17.5 = 27.5%

∴ Tin in second alloy = 27.5%

In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?
  • a)
    50
  • b)
    100
  • c)
    150
  • d)
    200
Correct answer is option 'C'. Can you explain this answer?

Gowri Chakraborty answered
Let x is the number of 25 paisa coins then 2x and 3x will be for 10 and 5 paisa coins. 

Now 30 rupees equal to 30*100 paisa now total paisa equal to x*25+2x*10+3x*5=3000.

60x = 3000.
x = 50.

Now number 5 paisa coin is 3x equal to 3*50 = 150.

The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?
  • a)
    72
  • b)
    132
  • c)
    60
  • d)
    66
Correct answer is option 'D'. Can you explain this answer?

Anaya Patel answered
Let the 1stno. A = X
2nd no.= B , 3rd no.= C , 4th no. = D

A: B =2:3
A/B = 2/3
x/B =2/3
B= 3x/2

B:C=5:6
(3x/2)/ C= 5/6
C=( 6×3x)/2×5= 9x/5
C= 9x/5

C:D= 8:9
9x/5/ D = 8/9
D= (9x×9)/8×5= 81x/40
D= 81x/40

A+B+C+D= 253. (GIVEN)
x+ 3x/2+9x/5+81x/40

Lcm = 40
(40x+ 60x+ 72x+81x)/40= 253
253x= 253×40
X= (253×40)/253= 40
Ist no.(A)= X= 40
2no.(B)= 3x/2=( 3 × 40)/2= 60
3rd no.(C)= 9x/5 = (9×40)/5= 72
4th no.(D)= 81x/40=( 81×40/)/40= 81

Average of numbers= sum of observations/ total no.of observations
Average of 2nd no. & 3rd no.= (60+72)/2= 132/2= 66

Four numbers in the ratio of 1:3:4:7 add up to give a sum of 75. Find the value of the biggest number.
  • a)
    42
  • b)
    35
  • c)
    49
  • d)
    63
Correct answer is option 'B'. Can you explain this answer?

Kavya Saxena answered
Method to Solve :

Let 1:3:4:7 be 1x, 3x, 4x, 7x respectively.
1x + 3x + 4x + 7x =75
15x = 75
x = 75/15
x = 5
So, 1x = 1*5 = 5
3x = 3*5 = 15
4x = 4*5 = 20
7x = 7*5 = 35

Can you explain the answer of this question below:

Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

  • A:

    27

  • B:

    33

  • C:

    49

  • D:

    55

The answer is B.

Sagar Sharma answered
Given:
The ratio of two numbers is 3:5
After subtracting 9 from each number, the new ratio is 12:23

Let's assume the two numbers in the original ratio are 3x and 5x.

Ratio of the new numbers:
(3x-9) : (5x-9) = 12 : 23

Cross-multiplying, we get:
12(5x-9) = 23(3x-9)

Simplifying the equation:
60x - 108 = 69x - 207
-9x = -99
x = 11

Finding the smaller number:
Smaller number = 3x = 3 * 11 = 33

Therefore, the smaller number is 33, which corresponds to option 'B'.

If 0.75 : x :: 5 : 8, then x is equal to:
  • a)
    1.12
  • b)
    1.2
  • c)
    1.25
  • d)
    1.30
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
To find the value of "x" in the given proportion 0.75 : x :: 5 : 8, we can use the concept of cross-multiplication.

Step 1: Set up the proportion
0.75 : x :: 5 : 8

Step 2: Cross-multiply
0.75 * 8 = x * 5

Step 3: Solve for "x"
6 = 5x

Step 4: Divide both sides by 5
x = 6 / 5

Step 5: Simplify the fraction
x = 1.2

Therefore, the value of "x" in the proportion 0.75 : x :: 5 : 8 is equal to 1.2.

Summary:
To find the value of "x" in the given proportion, we set up the proportion and cross-multiply. Then we solve for "x" by dividing both sides of the equation. In this case, the value of "x" is equal to 1.2.

Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?
  • a)
    6
  • b)
    12
  • c)
    15
  • d)
    21
Correct answer is option 'C'. Can you explain this answer?

Mihir Mehta answered
Understanding the Problem
We have two numbers in the ratio 2:5. Let's denote these numbers as:
- First Number = 2x
- Second Number = 5x
After adding 6 to both numbers, their ratio changes to 4:7.
Setting Up the Equation
When we add 6 to both numbers, we can express the new situation as:
- New First Number = 2x + 6
- New Second Number = 5x + 6
According to the problem, the new ratio is:
(2x + 6) / (5x + 6) = 4/7
Cross-Multiplying to Solve
To eliminate the fraction, we can cross-multiply:
7(2x + 6) = 4(5x + 6)
This simplifies to:
14x + 42 = 20x + 24
Rearranging the Equation
Next, we rearrange it to isolate x:
14x - 20x = 24 - 42
This gives us:
-6x = -18
Thus, we find:
x = 3
Finding the Numbers
Now that we have x, we can find the original numbers:
- First Number = 2x = 2(3) = 6
- Second Number = 5x = 5(3) = 15
Conclusion
The larger number is:
- 15
Thus, the correct answer is option 'C'.

A and B invested Rs 12,000 and Rs 18,000 respectively in a business for the whole year. At the year-end, there was a total profit of Rs 2,000. What is the share of A in the profit?
  • a)
    Rs 800
  • b)
    Rs 1,200
  • c)
    Rs 1,600
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Advait Saini answered
Investment Details
A and B have invested different amounts in a business:
- A's investment: Rs 12,000
- B's investment: Rs 18,000
Total Investment
- Total investment by both A and B = Rs 12,000 + Rs 18,000 = Rs 30,000
Profit Distribution
The total profit at the year-end is Rs 2,000. The profit is shared based on the ratio of their investments.
Calculating the Ratio
- A's investment = Rs 12,000
- B's investment = Rs 18,000
- Ratio of A’s investment to B’s investment = 12,000 : 18,000
To simplify:
- Divide both sides by 6
- A : B = 2 : 3
Finding A's Share in Profit
To determine A's share in the profit, we first calculate the total parts in the ratio. The total parts = 2 (for A) + 3 (for B) = 5 parts.
Next, we find out how much each part is worth:
- Value of each part = Total Profit / Total Parts = Rs 2,000 / 5 = Rs 400
Now, we can calculate A's share:
- A's share = 2 parts * Value of each part = 2 * Rs 400 = Rs 800
Conclusion
Thus, A's share in the profit is Rs 800, which corresponds to option 'A'.

In a fort there are 1600 soldiers fighting a battle against their enemy. On a particular day after their morning meal the balance provision inside the fort is only sufficient for 12 days at the rate of 1.2 kg per day. If by the evening 400 soldiers die then for how many days will the provision be sufficient for remaining men at the rate of 1.6 kg per day. (Assume soldiers eat either in morning or in evening).
  • a)
    10
  • b)
    8
  • c)
    18
  • d)
    12
Correct answer is option 'D'. Can you explain this answer?

Alok Verma answered
Total quantity of food at the beginning of the day
= (1600) (12) (1.2) 
Total number of soldiers left at the end of the day 1200
Now we have to calculate that for how long is available provision enough for the left-out soldiers
(1200) (x) (1.6)
(1600) (12) (1.2) = (1200) (x) (1.6)
Solving it for the value of x
We get x = 12
The provision is sufficient for 1200 soldiers for 12 days.

In a garrison of 3600 men, the provisions were sufficient for 20 days at the rate of 1.5 kg per man per day. If x more men joined, the provisions would be sufficient for 12 days at the rate of 2 kg per man per day. Find x.
  • a)
    600
  • b)
    800
  • c)
    900
  • d)
    720
Correct answer is option 'C'. Can you explain this answer?

Rhea Reddy answered
Let x be the number of new men joined the garrison,
The total quantity of food is = 3600(20) (1.5) kg ----------1
Now the available food will be consumed by (3600+x) men
(3600+x) (12) (2) kg  --------------2
1 = 2
Solving both the equations
3600(20) (1.5) = (3600+x) (12) (2)
108000 = 86400 + 24x
21600 = 24x
X = 900
900 more men joined the garrison.

A man has rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
  • a)
    100
  • b)
    50
  • c)
    78
  • d)
    90
Correct answer is option 'D'. Can you explain this answer?

Aisha Gupta answered
 Given that a man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal.
We are to find the total number of notes he has.
Let x represents the number of notes of each of the three denominations.
Then, according to the given information, we have

Two numbers are 30% and 20% less than a third number respectively. The ratio of first two numbers is:
  • a)
    7 : 6
  • b)
    3 : 2
  • c)
    7 : 8
  • d)
    8 : 7
Correct answer is option 'C'. Can you explain this answer?

Capstone Ias Learning answered
Given:
Two numbers are 30% and 20% less than a third number respectively.
Formula Used:
If a number is x% less than another number, then it is equal to (100 - x)% of that number.
Ratio = First number / Second number
Calculation:
Let the third number be 100.
First number = 100 - 30% of 100
First number = 100 - 30
First number = 70
Second number = 100 - 20% of 100
Second number = 100 - 20
Second number = 80
Ratio of the first two numbers = First number / Second number
⇒ Ratio = 70 / 80
⇒ Ratio = 7 / 8
The ratio of the first two numbers is 7 : 8.

Read the passage below and solve the questions based on it.
There are certain number of apples, guavas and oranges in a basket. The number of each variety is more than one. The ratio of the number of apples to the number of guavas is equal to the ratio of the number of guavas lo the number of oranges.
Q.
If the total number of fruits is 61, then find the number of guavas.
  • a)
    16
  • b)
    20
  • c)
    25
  • d)
    Cannot be determined
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Ratio of fruits in the basket:
- Let the number of apples be represented by A
- Let the number of guavas be represented by G
- Let the number of oranges be represented by O
- We know that A:G = G:O

Total number of fruits:
- The total number of fruits is given as 61
- Therefore, A + G + O = 61

Finding the number of guavas:
- We need to find the number of guavas, which is represented by G
- Since we know that A:G = G:O, we can write this as A/G = G/O
- Cross-multiplying, we get A*O = G*G
- We also know that A + G + O = 61
- Substituting A*O = G*G, we get G*G + G + G*O = 61G
- Simplifying, we get G^2 + G*O - 61G = 0
- Using the quadratic formula, we get G = 20 or G = 41
- Since the number of each variety is more than one, we can eliminate G = 41
- Therefore, the number of guavas is 20

Answer:
- Therefore, the correct option is (b) 20

P works twice as fast as Q, whereas P and Q together can work three times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?
  • a)
    2:1:1
  • b)
    4:2:1
  • c)
    4:3:2
  • d)
    4:2:3
Correct answer is option 'A'. Can you explain this answer?

Akanksha Datta answered
If P is taking 3 days to do some work, then Q takes 6 days to do the same work. Now, both of them will take 2 days to complete the work. So, R takes 6 days to complete the same work.
Hence, earning should be distributed in the ratio of their efficiency, i.e., 2 : 1 : 1.

A bottle contains 10 litres of Milk. 2 litres of Milk is taken out of it and replaced by same quantity of Water. Again 2 litres of the mixture is taken out and replaced by same quantity of Water. What is the ratio of quantity of water to that of Milk in the final mixture?
  • a)
    16 : 19
  • b)
    9 : 16
  • c)
    5 : 4
  • d)
    4 : 5
Correct answer is option 'B'. Can you explain this answer?

Maya Choudhary answered
Initial Setup
- Start with 10 litres of milk in the bottle.
First Replacement
- 2 litres of milk is removed:
- Remaining milk = 10 - 2 = 8 litres
- Add 2 litres of water:
- Total mixture = 8 litres of milk + 2 litres of water = 10 litres
Concentration After First Replacement
- Concentration of milk after first replacement:
- Milk = 8 litres
- Water = 2 litres
Second Replacement
- Take out 2 litres of the mixture (which contains both milk and water):
- The ratio of milk to water in the mixture = 8:2 or 4:1
- Total parts = 5 (4 parts milk + 1 part water)
- Amount of milk in 2 litres taken out:
- Milk taken out = (4/5) * 2 = 1.6 litres
- Amount of water in 2 litres taken out:
- Water taken out = (1/5) * 2 = 0.4 litres
Final Quantities
- Remaining milk = 8 - 1.6 = 6.4 litres
- Remaining water = 2 - 0.4 = 1.6 litres
- Add 2 litres of water to the mixture:
- Total water = 1.6 + 2 = 3.6 litres
Final Ratio of Water to Milk
- Final quantities:
- Milk = 6.4 litres
- Water = 3.6 litres
- Ratio of water to milk:
- Water : Milk = 3.6 : 6.4
- Simplifying this gives = 9 : 16
Correct Answer
- The final ratio of quantity of water to that of milk in the mixture is 9 : 16. Thus, the correct option is b.

A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?
  • a)
    60
  • b)
    80
  • c)
    100
  • d)
    120
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given:
Total number of coins = 220
Total amount = 160
Let the number of 25 paise coins be x
Let the number of 50 paise coins be y
Let the number of 1 Rupee coins be z

Equations:
1. x + y + z = 220 (Total number of coins)
2. 0.25x + 0.5y + z = 160 (Total amount)

Given that there are thrice as many 1 Rupee coins as there are 25 paise coins:
3. z = 3x

Substituting equation 3 in equation 1, we get:
x + y + 3x = 220
4x + y = 220

Substituting equation 3 and equation 2 in equation 1, we get:
0.25x + 0.5y + 3x = 160
3.25x + 0.5y = 160

Solving equations 4 and 5 simultaneously, we get:
x = 20
y = 60
z = 60

Therefore, the number of 50 paise coins is 60. Hence, the correct answer is option A.

The first, second and third class fares between two railway stations, Patna and Lucknow were 10:8:3 and the number of first, second and third class passengers between the two stations was is 3:4:10. If total sales of the ticket is Rs 16,100, find the money obtained by the sales of second class tickets.
  • a)
    Rs 5,250
  • b)
    Rs 5,600
  • c)
    Rs 6,400
  • d)
    Rs 6,650
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
To solve this problem, we need to use the concept of ratios and proportions. Let's break down the given information and solve step by step.

Given information:
- The ratio of first, second, and third class fares between Patna and Lucknow is 10:8:3.
- The ratio of first, second, and third class passengers between the two stations is 3:4:10.
- The total sales of tickets is Rs 16,100.

Step 1: Calculate the total ratio of fares.
The total ratio of fares can be found by adding up the individual ratios: 10 + 8 + 3 = 21.

Step 2: Calculate the proportion of each fare.
To find the proportion of each fare, divide each individual fare ratio by the total ratio of fares:
First class fare proportion = 10/21
Second class fare proportion = 8/21
Third class fare proportion = 3/21

Step 3: Calculate the total sales from each fare.
To find the total sales from each fare, multiply the total sales by the proportion of each fare:
Total sales from first class fare = (10/21) * Rs 16,100
Total sales from second class fare = (8/21) * Rs 16,100
Total sales from third class fare = (3/21) * Rs 16,100

Step 4: Calculate the money obtained by the sales of second class tickets.
From step 3, we can see that the total sales from second class fare is:
Total sales from second class fare = (8/21) * Rs 16,100

Simplifying this expression, we get:
Total sales from second class fare = Rs 5,600

Therefore, the money obtained by the sales of second class tickets is Rs 5,600, which corresponds to option B.

Chapter doubts & questions for Ratio & Proportion - CSAT Preparation 2025 is part of UPSC CSE exam preparation. The chapters have been prepared according to the UPSC CSE exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for UPSC CSE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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