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All questions of Ratio and Proportion for CTET & State TET 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.
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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.

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?

Future Foundation Institute answered
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 

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**.

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

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.

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'.

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?

Ashwini Chatterjee answered
**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?

Shilpa Choudhury answered
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.

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.

The salary of A, B and C are in the ratio of 5 : 11 : 6. If their total salary is Rs.2750, find the salary received by C?(in Rs)
  • a)
    752
  • b)
    753
  • c)
    751
  • d)
    750
Correct answer is option 'D'. Can you explain this answer?

TeamUnknown answered
Given:
A : B : C = 5 : 11 : 6
Total salary = Rs. 2,750
Calculation:
Salary received by C = 
 × 2750 = Rs. 750
∴ The salary received by C is Rs. 750.

In a box, there are ₹10 notes, ₹20 notes and ₹50 in a ratio of 3 ∶ 5 ∶ 7. The total amount of notes is ₹3,360. Find the number of ₹20 notes and ₹50 notes taken together.
  • a)
    84
  • b)
    79
  • c)
    80
  • d)
    73
Correct answer is option 'A'. Can you explain this answer?

Tech Era answered
Given:
There are ₹10 notes, ₹20 notes and ₹50 in a ratio of 3N ∶ 5N ∶ 7N.
The total amount of notes is ₹3,360.
Calculation:
According to question,
(10 × 3N) + 
(20 × 5N) + (50 × 7N) = 3360
⇒ 30N + 100N + 350N = 3360
⇒ 480N = 3360
⇒ N = 3360/480
⇒ N = 7
Now,
The number of ₹20 notes = 5 × 7 = 35
The number of ₹50 notes = 7 × 7 = 49
₹20 notes and ₹50 notes taken together:
⇒ 35 + 49 = 84
∴ The number of ₹20 notes and ₹50 notes taken together is 84.

The ratio of number of men and women in a ice-cream factory of 840 workers is 5 : 7. How many more men should be joined to make the ratio 1 : 1? 
  • a)
    240
  • b)
    200
  • c)
    190
  • d)
    140
Correct answer is option 'D'. Can you explain this answer?

Coders Trust answered
Shortcut Trick
Men : Women = 5 : 7
Total number of workers = 840
⇒ The value of 12 → 840
⇒ The value of 1 → 70
Since more men are joining. But the women are the same. 
⇒ The value of 2 → 70 × 2 = 140
Hence, 140 more men should be joined to make the ratio 1 : 1.
Alternate Method
Let the men and women in the ice-cream factory be 5x and 7x respectively.
⇒ 5x + 7x = 840
⇒ 12x = 840
⇒ x = 70
Thus, Men = 5x = 5 × 70 = 350
And women = 7x = 7 × 70 = 490
Let y more men should be joined to make the ratio 1 : 1.

⇒ 350 + y = 490
⇒ y = 140
Hence, 140 more men should be joined to make the ratio 1 : 1.

The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number 
  • a)
    200
  • b)
    120
  • c)
    50
  • d)
    160
Correct answer is option 'A'. Can you explain this answer?

Ritesh Kumar Shivhare answered
Given:
The sum of the three numbers = 370
The first number = 1/4th of the third number
The ratio of the second number to the third = 3 : 5
Calculation:
According to question
Let, 2nd number = 3X & 3rd number = 5X
And, 1st number = (1/4) × 5X = 5X/4
Now, (5X/4) + 3X + 5X = 370 
⇒ (5X/4) + 8X = 370 
⇒ 37X/4 = 370 
⇒ X
 = (370 × 4)/37 = 40
The third number = 5 × 40 = 200
∴ Correct answer is 200

x varies directly as the square of y and inversely as the cube root of z and x = 2, when y = 4, z= 8. What is the value of y when x = 3, and z = 27?
  • a)
    6, -6
  • b)
    4, -4
  • c)
    1, -1
  • d)
    5, -5
Correct answer is option 'A'. Can you explain this answer?

Ritesh Kumar Shivhare answered
Given:
Direct variation relationship = x ∝ y2.
Inverse variation relationship = x ∝ 1/z(1/3).
Concept used:
In variation problems, establishing the constant of proportionality allows transformation into equality.
Calculations:
x = k (y2/z(1/3)) where k is the constant of proportionality.
Substituting x = 2, y = 4, and z = 8
⇒  2 = k((42) ÷ (8(1/3)) 
⇒ k = 0.25
Now substituting x = 3, z = 27, and k = 0.25 
⇒ 3 = 0.25(y2/(27(1/3))).
⇒ 3 = 0.25(y2/3)
⇒ y2 = 900/25
⇒  y2 = ±36.
⇒ y = ±6.
∴ y can be either 6 or -6.

If 
 =
 and
 =
, then 
 is :
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?

Reeva Reeva answered
Simplify the 3 equations to the form a:b:c a/b =7/11 =84/132 b/c =12/17 =132/187 Hence, a:b:c = 84:132:187 Thus, (a+b)/(b+c) =(84+132)/(132+187) =216/319 Thus, Option D) 216/319 is correct

A bag has ₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins. The coins are in the ratio of 6 : 9 : 10. How many coins of ₹ 5 are in the bag?
  • a)
    60
  • b)
    12
  • c)
    45
  • d)
    24
Correct answer is option 'C'. Can you explain this answer?

Anjana Singh answered
Given:
₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins
The coins are in the ratio of 6 : 9 : 10
Calculation:
Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively
⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785
⇒ 157x = 785
∴ x = 5
Number of coins of ₹ 5 = 9x = 9 × 5 = 45
∴ 45 coins of ₹ 5 are in the bag

Two numbers are in ratio of 4 ∶ 5 respectively. If each number is reduced by 25, then the ratio becomes 3 ∶ 4. Find the largest number.
  • a)
    100
  • b)
    125
  • c)
    130
  • d)
    135
Correct answer is option 'B'. Can you explain this answer?

Tech Era answered
Given:
Original ratio of two numbers = 4 : 5
Modified ratio of two numbers = 3 : 4
Each number when reduced by 25
Calculation:
Let the original numbers be 4x and 5x.
According to the question,
 = 
⇒ 16x - 100 = 15x - 75
⇒ 16x - 15x = 100 - 75 
⇒ 
x = 25
Larger number = 5x = 5 × 25 = 125
∴ The largest number is 125.

What is the number of girls if the total number of students is 2400 and the ratio of boys to girls is 7:5?
  • a)
    2500
  • b)
    1000
  • c)
    1500
  • d)
    1550
Correct answer is option 'B'. Can you explain this answer?

Anil Kumar answered
Given:
Total students = 2400
Ratio of boys to girls = 7: 5
Concept used:
Total ratio units = sum of the ratio parts
Number of girls = (total students × girl's ratio units) / total ratio units
Calculation:
Total ratio units = 7 + 5 = 12
⇒ Number of girls = (2400 × 5) / 12
⇒ Number of girls = 12000 / 12
⇒ Number of girls = 1000
∴ The number of girls is 1000.
Alternate Method
Concept used:
Use the concept of proportional ratios.
Calculation:
Set up the ratio equation for girls (G) based on the given ratio:
Boys (B) : Girls (G) = 7 : 5
Express the ratio in terms of a variable (let x be the common multiplier):
B = 7x & G = 5x
Sum of the ratios equals the total number of students:
7x + 5x = 2400
Combine like terms:
12x = 2400
⇒ x = 200
Find the number of girls (G):
G = 5 × 200
⇒ G = 1000
∴ The number of girls is 1000.

Ravi, Ramesh and Suresh can work together for ₹1,680. If Ravi and Ramesh together are to do
 of the work, then the share (in ₹) of the Suresh should be:
  • a)
    825
  • b)
    945
  • c)
    975
  • d)
    735
Correct answer is option 'D'. Can you explain this answer?

Ritesh Kumar Shivhare answered
Given:
Ravi, Ramesh and Suresh can work together for ₹1,680
Ravi and Ramesh together are to do 
 of the work
Formula used:
The amount paid is directly proportional to the fraction of work done.
Efficiency = 1/time.
Solution:
According to the above formula:
The amount paid to 
Ravi and Ramesh together = 9/16 × 1680 = 945
The amount paid to Suresh = 1680 - 945 = 735
∴ The share of Suresh is 735.

If A ∶ B ∶ C = 2 ∶ 3 ∶ 4  then
 ∶ 
∶ 
 is equal to -
  • a)
    4 ∶ 9 ∶ 16
  • b)
    8 ∶ 9 ∶ 12
  • c)
    8 ∶ 9 ∶ 16
  • d)
    8 ∶ 9 ∶ 24
Correct answer is option 'D'. Can you explain this answer?

TeamUnknown answered
Given:
A ∶ B ∶ C = 2 ∶ 3 ∶ 4
Calculation:
Let A = 2x , B = 3x and C = 4x
Finds the value of this given expression  
 ∶ 
 ∶ 
 ,
The value of 
⇒ 
 = (2x/3x)
⇒ 
 = (2/3)
The value of 
⇒ 
 = (3x/4x)
⇒ 
 = (3/4)
The value of 
⇒ 
 = (4x/2x)
⇒ 
 = (2/1)
 ⇒ 
 ∶ 

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