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All questions of Ratio and Proportion for Civil Engineering (CE) Exam

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The ratio of age of Krish and her mother is 5:12 and difference of their ages is 21. What will be the ratio of their ages after 3 years ?
a)7:15
b)11:5
c)13:7
d)6:13
e)None of these
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Given: The ratio of age of Krish and her mother is 5:12 and difference of their ages is 21.

Let the age of Krish be 5x and the age of her mother be 12x.

Then, 12x - 5x = 21

Solving for x, we get x = 3.

So, Krish's age = 5x = 15 years and her mother's age = 12x = 36 years.

After 3 years, Krish's age will be 18 years and her mother's age will be 39 years.

Therefore, the required ratio of their ages after 3 years = 18:39 = 6:13.

Hence, the correct answer is option D) 6:13.

Section A and section B of 7th class in a school contains total 285 students.Which of the following can be a ratio of the ratio of the number of boys and number of girls in the class?
  • a)
    6 : 5
  • b)
    10 : 9
  • c)
    11 : 9
  • d)
    13 : 12
  • e)
    Cannot be determined
Correct answer is option 'B'. Can you explain this answer?

Faizan Khan answered
B) 10 : 9
Explanation: The number of boys and girls cannot be in decimal values, so the denominator should completely divide number of students (285).
Check each option: 6+5 = 11, and 11 does not divide 285 completely. 10+9 = 19, and only 19 divides 285 completely among all.

One year ago the ratio between rahul salary and rohit salary is 4:5. The ratio between their individual salary of the last year and current year is 2:3 and 3:5 respectively. If the total current salary of rahul and rohit is 4300. Then find the current salary of rahul.
  • a)
    1200
  • b)
    1800
  • c)
    1600
  • d)
    2000
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Faizan Khan answered
Answer – B.1800 Explanation : 4x and 5x is the last year salry of rahul and rohit respectively Rahul last year to rahul current year = 2/3 Rohit last year to rohit current year = 3/5 Current of rahul + current of rohit = 4300 (3/2)*4x + (5/3)*5x = 4300.
X = 300.
So rahul current salary  = 3/2 * 4* 300 = 1800

A, B and C divide Rs 4200 among themselves in the ratio 7 : 8 : 6. If Rs 200 is added to each of their shares, what is the new ratio in which they will receive the money?
  • a)
    9 : 8 : 7
  • b)
    8 : 9 : 7
  • c)
    8 : 9 : 8
  • d)
    9 : 10 : 8
  • e)
    7 : 9 : 8
Correct answer is option 'B'. Can you explain this answer?

Alok Verma answered
B) 8 : 9 : 7
Explanation: A gets = [7/(7+8+6)] * 4200 = 1400 B gets = [8/(7+8+6)] * 4200 = 1600 C gets = [6/(7+8+6)] * 4200 = 1200 Rs 200 added to each share, so new ratio = 1400+200 : 1600+200 : 1200+200
1600 : 1800 : 1400

A sum of Rs 315 consists of 25 paise, 50 paise and 1 Re coins in the ratio 3 : 4 :6. What is the number of each kind of coin respectively?.
  • a)
    216, 144, 27
  • b)
    108, 144, 216
  • c)
    27, 72, 216
  • d)
    120, 35, 108
  • e)
    102, 150, 210
Correct answer is option 'B'. Can you explain this answer?

Kavya Saxena answered
B) 108, 144, 216
Explanation: 25 paise = 25/100 Rs, 50 paise = 50/100 Rs So value ratio of these coins become = 3*(25/100) : 4*(50/100) : 6*(1) = 3/4 : 2 : 6 = 3 : 8 : 24
So 25 paise coins value= [3/(3+8+24)] * 315 = Rs 27, so coins = 27 * (100/25) = 108
Similarly find others.

An employer reduces the number of his employees in the ratio of 7:4 and increases their wages in the ratio 3:5. State whether his bill of total wages increases or decreases and in what ratio.
  • a)
    increases 20:21
  • b)
    decreases 21:20
  • c)
    increases 21:22
  • d)
    decreases 22:21
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given data:
- The number of employees is reduced in the ratio 7:4.
- The wages are increased in the ratio 3:5.

Let's assume that the employer had 7x employees and was paying each employee 5y wages.

After the reduction in the number of employees, the new number of employees will be 4x. But the wages have been increased in the ratio 3:5. Therefore, the new wage will be (5y * 5)/(3) = 25y/3.

So, the total bill of wages before the reduction = 7x * 5y = 35xy
And, the total bill of wages after the reduction = 4x * (25y/3) = (100xy/3)

Now, let's simplify the two bills of wages and see how they compare:

(100/3)xy - 35xy = (65/3)xy

So, the bill of total wages has decreased by (65/3)xy.

We can write this as a ratio of the two bills of wages:

New bill : Old bill = (100/3)xy : 35xy
= 100:105
= 20:21

Therefore, the correct option is (b) decreases 21:20.

The income of riya and priya are in the ratio of 4:5 and their expenditure is in the ratio of 2:3. If each of them saves 2000, then find their income.
  • a)
    4000, 6000
  • b)
    4000, 5000
  • c)
    5000, 4000
  • d)
    5000, 6000
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given:
Income ratio of Riya and Priya = 4:5
Expenditure ratio of Riya and Priya = 2:3
Savings of each = $2000

To find:
Income of Riya and Priya

Solution:
Let the income of Riya be 4x and the income of Priya be 5x.
Let the expenditure of Riya be 2y and the expenditure of Priya be 3y.

Since the savings of each is $2000, we can write the equation as:
4x - 2y = 2000 ...(1)
5x - 3y = 2000 ...(2)

Now, we need to solve these two equations to find the values of x and y.

Simplifying equation (1) by dividing both sides by 2, we get:
2x - y = 1000

Multiplying equation (2) by 2, we get:
10x - 6y = 4000

Now, we have two equations:
2x - y = 1000 ...(3)
10x - 6y = 4000 ...(4)

Multiplying equation (3) by 6 and equation (4) by 1, we get:
12x - 6y = 6000 ...(5)
10x - 6y = 4000 ...(6)

Now, subtracting equation (6) from equation (5), we get:
(12x - 6y) - (10x - 6y) = 6000 - 4000
2x = 2000
x = 1000

Substituting the value of x in equation (1), we can find y:
4x - 2y = 2000
4(1000) - 2y = 2000
4000 - 2y = 2000
-2y = -2000
y = 1000

Therefore, the income of Riya is 4x = 4(1000) = $4000 and the income of Priya is 5x = 5(1000) = $5000.

Hence, the correct answer is option B) 4000, 5000.

An amount of money is to be distributed among P, Q and R in the ratio of 7:4:5 respectively. If the total share of P and R is 4 times the share of Q, what is definitely Q’s share?
  • a)
    2000
  • b)
    4000
  • c)
    6000
  • d)
    Data inadequate
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Cstoppers Instructors answered

The given ratio is:
A : B : C = 3 : 5 : 7
Let the common factor be x. Thus, the production units will be:
A = 3x
B = 5x
C = 7x
We are also given that the total production is 30,000 units. So:
3x + 5x + 7x = 30,000
15x = 30,000
x = 2,000
Now, substitute x = 2,000 into the expressions for each product:
A's production = 3 × 2,000 = 6,000 units
B's production = 5 × 2,000 = 10,000 units
C's production = 7 × 2,000 = 14,000 units
So, the production for A, B, and C is:
A = 6,000 units
B = 10,000 units
C = 14,000 units
Final Answer:
Initial production:
A = 6,000 units, B = 10,000 units, C = 14,000 units
 

Three cars travel same distance with speeds in the ratio 2 : 4 : 7. What is the ratio of the times taken by them to cover the distance?
  • a)
    12 : 6 : 7
  • b)
    14 : 7 : 4
  • c)
    10 : 5 : 9
  • d)
    7 : 4 : 14
  • e)
    14 : 10 : 7
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Ratio of speeds of three cars = 2 : 4 : 7

Let us assume that the distance covered by each car is equal to ‘d’ units.

Let the time taken by each car to cover this distance be ‘t1’, ‘t2’ and ‘t3’ units.

We know that,

Speed = Distance / Time

Therefore,

t1 = d/2, t2 = d/4 and t3 = d/7

Ratio of time taken by each car to cover the distance = t1 : t2 : t3

= d/2 : d/4 : d/7

= 7d/14 : 3.5d/14 : 2d/14

= 14 : 7 : 4

Hence, the correct answer is option B) 14 : 7 : 4.

Rs 650 was divided among 3 children in the ratio 2 : 4 : 7. Had it been divided in the ratio 1/2 : 1/4 : 1/7, who would have gained the most and by how much?
  • a)
    C, Rs 246
  • b)
    C, Rs 264
  • c)
    B, Rs 18
  • d)
    A, Rs 246
  • e)
    A, Rs 264
Correct answer is option 'E'. Can you explain this answer?

Anaya Patel answered
E) A, Rs 264 Explanation: New ratio = 1/2 : 1/4 : 1/7 = 14 : 7 : 4 So both ratio suggests that C has not gained any money, rather he has lose the money.
For both ratio find the shares of A and B With ratio 2 : 4 : 7, A gets = [2/(2+4+7)] * 650 = 100, B gets = [4/(2+4+7)] * 650 = 200
With ratio 14 : 7 : 4, A gets = [14/(14+7+4)] * 650 = 364, B gets = [7/(14+7+4)] * 650 = 182
B has also lose the money, A gain the money and = 364 – 100 = 264

Number of students in 4th and 5th class is in the ratio 6 : 11. 40% in class 4 are girls and 48% in class 5 are girls. What percentage of students in both the classes are boys?
  • a)
    62.5%
  • b)
    54.8%
  • c)
    52.6%
  • d)
    55.8%
  • e)
    53.5%
Correct answer is option 'B'. Can you explain this answer?

KS Coaching Center answered
B) 54.8%
Explanation: Total students in both = 6x+11x = 17x Boys in class 4 = (60/100)*6x = 360x/100 Boys in class 5 = (52/100)*11x = 572x/100 So total boys = 360x/100 + 572x/100 = 932x/100 = 9.32x % of boys = [9.32x/17x] * 100

The income of Neha and Hitesh are in the ratio of 4:5 and their expenditure is in the ratio of 2:3. If each of them saves 2000, then find their income.
  • a)
    4000, 6000
  • b)
    4000, 5000
  • c)
    5000, 4000
  • d)
    5000, 6000
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given, the income ratio of Neha and Hitesh is 4:5 and their expenditure ratio is 2:3. Let the income of Neha and Hitesh be 4x and 5x respectively.

Savings of Neha = Income of Neha - Expenditure of Neha = 4x/2 - 2y/2 = 2x - y
Savings of Hitesh = Income of Hitesh - Expenditure of Hitesh = 5x/3 - 3y/3 = 5x/3 - y

Given, their savings are equal and is 2000 each. Therefore, we have 2x - y = 2000 and 5x/3 - y = 2000.

On solving these equations, we get x = 3000 and y = 2000.

Therefore, the income of Neha and Hitesh are 4x = 4(3000) = 12000 and 5x = 5(3000) = 15000 respectively.

Hence, the correct answer is option B) 4000, 5000.

Equal quantities of 3 mixtures of milk and water are mixed in the ratio 1:3, 2:3 and 3:4.The ratio of water and milk in the new mixture is
  • a)
    45:76
  • b)
    151:269
  • c)
    123:154
  • d)
    145:245
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Alok Verma answered
Answer – B.151:269 Explanation : Milk = 1/4 : 2/5 :3/7 = 35/140 :56/140 : 60/140
Quantity of milk in new mix = 35+56+60 = 151 Quantity of water in new mix = 140*3 = 420-151 = 269 M:W = 151:269

The income of Vinay and Prakash are in the ratio of 4:5 and their expenditure is in the ratio of 2:3. If each of them saves 5000, then find their income.
  • a)
    7500, 10000
  • b)
    12500, 10000
  • c)
    10000, 12500
  • d)
    12500, 7500
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
Given information:
- The income of Vinay and Prakash are in the ratio of 4:5.
- Their expenditure is in the ratio of 2:3.
- Each of them saves 5000.

Let's assume the income of Vinay and Prakash as 4x and 5x respectively.
Similarly, let's assume the expenditure of Vinay and Prakash as 2y and 3y respectively.

According to the given information, we can write the following equations:
4x - 2y = 5000 ----(1) (Vinay's savings)
5x - 3y = 5000 ----(2) (Prakash's savings)

To solve these equations, we can use the method of substitution or elimination.

Using elimination method:
Multiply equation (1) by 3 and equation (2) by 2 to eliminate 'y':
12x - 6y = 15000 ----(3)
10x - 6y = 10000 ----(4)

Subtract equation (4) from equation (3):
(12x - 6y) - (10x - 6y) = 15000 - 10000
2x = 5000
x = 2500

Substitute the value of x in equation (1) to find y:
4(2500) - 2y = 5000
10000 - 2y = 5000
-2y = 5000 - 10000
-2y = -5000
y = 2500

So, the income of Vinay is 4x = 4(2500) = 10000 and the income of Prakash is 5x = 5(2500) = 12500.

Therefore, the correct answer is option C) 10000, 12500.

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