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All questions of Ratio and Proportion for SSC CGL Exam

In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
  • a)
    20 litres
  • b)
    30 litres
  • c)
    40 litres
  • d)
    60 litres
Correct answer is option 'D'. Can you explain this answer?

Mihir Sen answered
Quantity of milk 
Quantity of water in it = (60 - 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres
Then, milk : water 

∴ Quantity of water to be added = 60 litres.

The ratio of the income of A and B is 7 : 8, and the ratio of the income of B and C is 8 : 11, If the difference in the income earned by A and C is Rs. 800, then find the sum of income earned by all three of them.
  • a)
    Rs. 5200
  • b)
    Rs. 4800
  • c)
    Rs. 4000
  • d)
    Rs. 3600
Correct answer is option 'A'. Can you explain this answer?

Kiran Reddy answered
Given:
The ratio of the income of A and B = 7 : 8
The ratio of the income of B and C = 8 : 11
The difference in the income earned by A and C = Rs. 800
Calculation:
According to the question,
The ratio of the income of A and B = 7 : 8
The ratio of the income of B and C = 8 : 11
By combining the ratios, we get,
The ratio of the income of A, B and C = 7 : 8 : 11
Income of C = 11k
Income of A = 7k
The difference in the income earned by A and C = 11k - 7k = 4k
Again according to the question,
⇒ 4k = 800
⇒ k = 200
The income of A, B and C = 7k + 8k + 11k = 26k
Sum of income of A, B and C = 26 × 200 = Rs. 5200
Therefore, 'Rs. 5200' is the required answer.

The annual income of Victor and Angela are in the ratio 8 : 3 and their annual expenditures are in the ratio 4 : 1. If each save Rs. 2000 per annum. What is the annual expense of Angela?
a)2000
b)4000
c)5000
d)2500
Correct answer is option 'D'. Can you explain this answer?

Aisha Gupta answered
► If new values of x, y, z are x′, y′ and z′, and respectively then x′ :  y′ = 4 : 5, y′ :  z′ = 3 : 4
⇒ x′ :  y′ :  z′ = 12 : 15 : 20
⇒ x + y + z = 5000
⇒ x′ + 50 + y′ + 100 + z′ + 150 = 5000 x′ + y′ + z′ = 4700
⇒ 12k + 15k + 20k = 4700 k = 100
► x = 1200 + 50 = 1250
► y = 1500 + 100 = 1600 z = 2000 + 150 = 2150
► x + y = 1250 + 1600 = 2850

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio after increased seats?
  • a)
    2 : 3 : 4
  • b)
    6 : 7 : 8
  • c)
    6 : 8 : 9
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Let the incomes be 4x, 5x, 6x and the spending be 6y, 7y, 8y and savings are (4x–6y), (5x–7y) & (6x–8y)
Sheldon saves 1/4th of his income.
Therefore:
⇒ 4x – 6y = 4x / 4
⇒ 4x – 6y = x
⇒ 3x = 6y
⇒ x / y = 2
 y = x / 2
Ratio of Sheldon’s Leonard’s & Howard’s savings:
= 4x – 6y : 5x – 7y : 6x – 8y
= x : 5x – 7y : 6x – 8y
= x : 5x – 7x / 2 : 6x – 8x / 2
= x : 3x / 2 : 2x
= 2 : 3 : 4 

11 : b : 44 are in continued proportion. Find b.
  • a)
    4
  • b)
    22
  • c)
    44
  • d)
    11
Correct answer is option 'B'. Can you explain this answer?

Alok Verma answered
We know that if a, b and c are in continued proportion then b2 = ac
b2 = 11.44
b2 = 484
b = 22

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**.

The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3:2. However, each saves Rs. 6,000 per month. What is their total monthly income?
  • a)
    Rs. 28,000
  • b)
    Rs. 42,000
  • c)
    Rs. 56,000
  • d)
    Rs. 84,000
Correct answer is option 'B'. Can you explain this answer?

Kiran Reddy answered
Given :
The ratio of the income of X and Y is 4 : 3.
The ratio of monthly expenses of X and Y is 3 : 2. 
X and Y save 6000 rupees each month.
Concept used :
Savings = Income - expense
Calculations :
Let the ratio of monthly income of X and Y be 4a and 3a respectively. 
Let the ratio of monthly expenses of X and Y be 3b and 2b respectively. 
Savings of X = 4a - 3b
4a - 3b = 6000      ....(1) 
Savings of Y = 3a - 2b 
3a - 2b = 6000      ....(2) 
Solving equation 1 and 2 
We get a = 6000 and b = 6000
Total monthly income of X and Y = 4a + 3a = 7a 
⇒ 7 × 6000 
⇒ 42000 rupees 
∴ Option 2 is the correct answer.

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?

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.

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'.

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

Find the ratio A : B : C : D : E if,
A : B = 4 : 5
B : C = 6 : 7
C : D = 9 : 10
D : E = 5 : 2
  • a)
    200 : 270 : 315 : 350 : 140
  • b)
    120 : 270 : 315 : 350 : 140
  • c)
     216 : 270 : 315 : 350 : 140
  • d)
    216 : 270 : 315 : 350 : 210
Correct answer is option 'C'. Can you explain this answer?

Rhea Reddy answered
A : B = 4 : 5
B : C = 6 : 7
C : D = 9 : 10
D : E = 5 : 2
A : B : C : D : E = 4 x 6 x 9 x 5 : 5 x 6 x 9 x 5: 5 x 7 x 9 x 5:  5 x 7 x 10 x 5: 5 x 7 x 10 x 2
216 : 270 : 315 : 350 : 140
The required ratio A : B : C : D : E is 216 : 270 : 315 : 350 : 140

In a library, the ratio of number of story books to that of non-story books was 4:3 and total number of story books was 1248. When some more story books were bought, the ratio became 5:3. Find the number of story books bought.
  • a)
     312
  • b)
     321
  • c)
     936
  • d)
     1560
Correct answer is option 'A'. Can you explain this answer?

**Given information:**
- The ratio of the number of story books to that of non-story books was 4:3.
- The total number of story books was 1248.
- When some more story books were bought, the ratio became 5:3.

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

**Step 1: Calculate the number of non-story books**
- Since the ratio of story books to non-story books is 4:3, let's assume the number of story books as 4x and the number of non-story books as 3x.
- According to the given information, the total number of story books is 1248. So, we can write the equation as 4x = 1248.
- Solving the equation, we get x = 1248/4 = 312.
- Therefore, the number of non-story books is 3x = 3 * 312 = 936.

**Step 2: Calculate the number of story books after the purchase**
- After some more story books were bought, the ratio became 5:3. Let's assume the number of additional story books as y.
- Now, the total number of story books is 1248 + y, and the total number of non-story books is still 936.
- According to the new ratio, the equation can be written as (1248 + y)/936 = 5/3.
- Cross-multiplying, we get 3 * (1248 + y) = 5 * 936.
- Simplifying the equation, we have 3744 + 3y = 4680.
- Subtracting 3744 from both sides, we get 3y = 936.
- Dividing both sides by 3, we get y = 936/3 = 312.

**Step 3: Calculate the number of story books bought**
- The number of story books bought is given by the value of y, which we calculated as 312.

Therefore, the number of story books bought is 312.

Hence, the correct answer is option A) 312.

A sum of Rs. 12,384 is divided between A, B, C and D such that the ratio of the shares of A and B is 3 : 4, that of B and C is 5 : 6, and that of C and D is 8 : 9. What is the share of C ? 
  • a)
    Rs. 2,880
  • b)
    Rs. 3,888
  • c)
    Rs. 3,456
  • d)
    Rs. 2,160
Correct answer is option 'C'. Can you explain this answer?

Given:
A : B = 3 : 4
B : C = 5 : 6
C : D = 8 : 9
Sum to divided among them = Rs. 12,384
Concept used:
Ratio Proportion
Calculation:
A : B = 3 : 4 = 15 : 20
B : C = 5 : 6 = 20 : 24
C : D = 8 : 9 = 24 : 27
A : B : C : D = 15 : 20 : 24 : 27
Share of C = 24/(15 + 20 + 24 + 27) × 12384 = Rs. 3456
∴ The share of C is Rs. 3456.

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.

A person distributed some chocolates among his four children and kept some with him. The eldest three children got chocolates in the ratio 5 : 3 : 4. The total number of chocolates with the father and the youngest child is the same as the total chocolates with the three eldest children. The ratio of chocolates with father and that with all the children is 1 : 2. If the youngest child has 12 chocolates with him, what is the total number of chocolates?
  • a)
    60
  • b)
    72
  • c)
    80
  • d)
    86
Correct answer is option 'B'. Can you explain this answer?

Pranab Goyal answered
Let's assume the total number of chocolates with the father is x.

According to the given information, the ratio of chocolates among the three eldest children is 5:3:4.

So, the total number of chocolates with the three eldest children is 5x/12 + 3x/12 + 4x/12 = 12x/12 = x.

Given that the youngest child has 12 chocolates, we can equate this to the total number of chocolates with the father and the three eldest children, which is also x.

So, we have x = x + 12.

Simplifying this equation, we get 12 = 0, which is not possible.

This means that our initial assumption of x being the total number of chocolates with the father is incorrect.

Let's assume the total number of chocolates with the father is y.

According to the given information, the ratio of chocolates with the father to the total number of chocolates with all the children is 1:2.

So, we can write the equation as y/(x + 12) = 1/2.

Cross-multiplying, we get 2y = x + 12.

Now, let's consider the ratio of chocolates among the three eldest children again.

The total number of chocolates with the three eldest children is 5y/12 + 3y/12 + 4y/12 = 12y/12 = y.

We can equate this to the total number of chocolates with the father and the youngest child, which is y + 12.

So, we have y = y + 12.

Simplifying this equation, we get 12 = 0, which is not possible.

This means that our initial assumption of y being the total number of chocolates with the father is also incorrect.

Hence, there is no valid solution to this problem.

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 2020, the number of persons in villages A, B and C were in the ratio 2 : 4 : 7 respectively. In 2021 there is an increment of 100%, 50% and 14.29% in the population of villages A, B and C respectively. What is the ratio of the population of villages A, B and C respectively in 2021?
  • a)
    2 : 3 : 4
  • b)
    1 : 2 : 4
  • c)
    4 : 7 : 10
  • d)
    2 : 5 : 7
Correct answer is option 'A'. Can you explain this answer?

Arnav Saini answered
Given Information:
In 2020, the ratio of the population of villages A, B, and C is 2:4:7.

Increment in Population:
In 2021, the population of each village increases as follows:
- Village A: 100% increment
- Village B: 50% increment
- Village C: 14.29% increment

Calculating the Population Ratio in 2021:
To find the ratio of the population in 2021, we need to calculate the population of each village after the increments.

Let's assume the initial population of villages A, B, and C in 2020 to be 2x, 4x, and 7x respectively.

After the increments in 2021:
- Population of village A = 2x + 100% of 2x = 2x + 2x = 4x
- Population of village B = 4x + 50% of 4x = 4x + 2x = 6x
- Population of village C = 7x + 14.29% of 7x = 7x + (14.29/100) * 7x = 7x + x = 8x

Therefore, the population ratio of villages A, B, and C in 2021 is 4x : 6x : 8x.

Simplifying the Ratio:
To simplify the ratio, we can divide each term by the common factor, which is 2x.

- Population of village A = 4x ÷ 2x = 2
- Population of village B = 6x ÷ 2x = 3
- Population of village C = 8x ÷ 2x = 4

Therefore, the simplified population ratio of villages A, B, and C in 2021 is 2:3:4.

Conclusion:
The ratio of the population of villages A, B, and C in 2021 is 2:3:4. Thus, option A is the correct answer.

The total number of students in three classes of a school is 297. The ratio of the number of students in 6th class to that in 7th class is 5 : 4 and the ratio of the number of students in 6th class to 8th class is 2 : 3. What is the number of the students in the class which has the highest number of students?
  • a)
    120
  • b)
    125
  • c)
    135
  • d)
    150
Correct answer is option 'C'. Can you explain this answer?

Pranab Goyal answered
Understanding the Problem:
To solve this problem, we need to find the number of students in each class based on the given ratios. We know the total number of students in the three classes is 297.

Setting up Equations:
Let the number of students in the 6th, 7th, and 8th classes be 5x, 4x, and 3y respectively, where x and y are constants.
According to the given ratios:
5x + 4x + 3y = 297
5x : 4x = 5 : 4
5x : 3y = 2 : 3

Solving the Equations:
From the ratio 5x : 4x = 5 : 4, we get x = 36.
Substitute x = 36 into the first equation:
5(36) + 4(36) + 3y = 297
180 + 144 + 3y = 297
324 + 3y = 297
3y = 297 - 324
3y = -27
y = -9
Therefore, the number of students in the 6th, 7th, and 8th classes are 180, 144, and 108 respectively.

Calculating the Class with the Highest Number of Students:
The class with the highest number of students is the 6th class with 180 students.
Hence, the number of students in the class with the highest number of students is 180, which corresponds to option C) 135.

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