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All questions of Ratio & Proportion, Percentage for SSC CHSL Exam

Weight of A and B are in the ratio of 3:5. If the weight of A is increased by 20 percent and then the total weight becomes 132 kg with an increase of 10 percent. B weight is increased by what percent.
  • a)
    2%
  • b)
    3%
  • c)
    4%
  • d)
    5%
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Answer – 3. 4% Explanation : Weight of A and B are 3x and 5x.
Initial weight before increase = (132*100)/110 = 120 8x = 120. X = 15 Initial weight of A and B are 45 and 75 kg respectively.
New weight of A = 54 so weight of B = 132 – 54 = 78.
So % increase = [(78-75)/75]*100 = 4 %

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.

 A vendor sells 50 percent of apples he had and throws away 20 percent of the remainder. Next day he sells 60 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
  • a)
    20%
  • b)
    22%
  • c)
    24%
  • d)
    26%
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Let the total number of apples the vendor initially had be 100 (for simplicity).
On the first day:
The vendor sells 50% of the apples:
Apples sold on day 1 = 50% of 100 = 50
The remaining apples after selling 50% are:
Remaining apples = 100 − 50 = 50
He then throws away 20% of the remaining apples:
Apples thrown away on day 1 = 20% of 50 = 10
The remaining apples after throwing away 20% are:
Remaining apples after day 1 = 50 − 10 = 40
On the second day:
The vendor sells 60% of the remaining apples:
Apples sold on day 2 = 60% of 40 = 24
The remaining apples after selling 60% are:
Remaining apples after selling on day 2 = 40 − 24 = 16
He throws away the rest, which is 16 apples.
Total apples thrown away:
Apples thrown away on day 1 = 10
Apples thrown away on day 2 = 16
Total apples thrown away = 10 + 16 = 26
Percentage of apples thrown away:

Thus, the vendor throws away 26% of his apples.

In a library, 30% of the books are in History. 50% of the remaining are in English and 40% of the remaining are in German. The remaining 4200 books are in regional languages. What is the total number of books in library?
  • a)
    10000
  • b)
    15000
  • c)
    20000
  • d)
    25000
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Let the total number of books in the library be T.
30% of the books are in History:
History books = 30% of T = 0.30 × T
The remaining books after accounting for History are:
Remaining books = T − 0.30 × T = 0.70 × T
50% of the remaining books are in English:
English books = 50% of the remaining = 0.50 × 0.70 × T = 0.35 × T
After accounting for English books, the remaining books are:
Remaining books after English = 0.70T − 0.35T = 0.35T
40% of the remaining books are in German:
German books = 40% of the remaining = 0.40 × 0.35 × T = 0.14 × T
After accounting for German books, the remaining books are:
Remaining books after German = 0.35T − 0.14T = 0.21T
The remaining 4200 books are in regional languages, so:
0.21 × T = 4200
Solving for T:
T = 4200/0.21 = 20000
Thus, the total number of books in the library is 20,000.

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?

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.

When the price of rice is increased by 25 percent, a family reduces its consumption such that the expenditure is only 10 percent more than before. If 40 kg of rice is consumed by family before, then find the new consumption of family.
  • a)
    34.2
  • b)
    35.2
  • c)
    36.2
  • d)
    37.2
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given information:
- Price of rice increased by 25%
- Family reduces consumption such that expenditure is only 10% more than before
- 40 kg of rice consumed by family before

To find:
- New consumption of family

Solution:
Let's assume the initial price of rice was $1 per kg.
Therefore, before the price increase, the family was spending $40 (40 kg x $1/kg) on rice.

After the price increase of 25%, the new price of rice becomes $1.25 per kg.
Now, if the family wants to spend only 10% more than before, they will have to spend $44 ($40 + 10% of $40) on rice.

We can use this information to find the new consumption of rice as follows:
- Let the new consumption of rice be x kg
- Then, the total expenditure on rice after the price increase will be $1.25x
- We know that $1.25x = $44 (the family's new expenditure on rice)
- Solving for x, we get x = 35.2 kg

Therefore, the new consumption of the family is 35.2 kg.

Answer: Option B) 35.2.

40% of the women are above 30 years of age and 80 percent of the women are less than or equal to 50 years of age. 20 percent of all women play basketball.If 30 percent of the women above the age of 50 plays basketball, what percent of players are less than or equal to 50 years?
  • a)
    50%
  • b)
    60%
  • c)
    70%
  • d)
    80%
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Let the total number of women be 100 (for simplicity).
Women above 30 years of age:
40% of the women are above 30 years of age, which means:
Women above 30 years = 40% of 100 = 40 women
Women less than or equal to 50 years of age:
80% of the women are less than or equal to 50 years of age, which means:
Women less than or equal to 50 years = 80% of 100 = 80 women
Women above 50 years of age:
Since 80% are less than or equal to 50 years, the remaining 20% are above 50 years of age, which means:
Women above 50 years = 20% of 100 = 20 women
Women who play basketball:
20% of all women play basketball, which means:
Total basketball players = 20% of 100 = 20 women
Women above 50 years of age who play basketball:
30% of the women above 50 years play basketball, which means:
Basketball players above 50 years = 30% of 20 = 6 women
Women less than or equal to 50 years who play basketball:
The total number of basketball players is 20, and 6 of them are above 50 years of age.
Therefore, the number of players less than or equal to 50 years of age is:
Basketball players less than or equal to 50 years = 20 − 6 = 14 women
Percentage of players who are less than or equal to 50 years of age:
Percentage of players less than or equal to 50 years = 
Thus, 70% of the basketball players are less than or equal to 50 years of age.

 60 percent of the employees of a company are women and 75% of the women earn 20000 or more in a month. Total number of employees who earns more than 20000 per month in the company is 60 percent of the total employees.What fraction of men earns less than 20000 per month?
  • a)
    5/8
  • b)
    5/7
  • c)
    1/5
  • d)
    3/4
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Total employees = 100 (for simplicity).
Number of women = 60% of 100 = 60 women.
Number of men = 40% of 100 = 40 men.
75% of the women earn 20,000 or more:
Women earning 20,000 or more = 75% of 60 = 0.75 × 60 = 45 women.
Total number of employees earning more than 20,000 per month is 60% of the total employees:
Employees earning more than 20,000 = 60% of 100 = 60 employees.
Out of these 60 employees, 45 are women, so the remaining 15 must be men:
Men earning more than 20,000 = 15 men.
The total number of men is 40, and 15 men earn more than 20,000, so the number of men earning less than 20,000 is:
Men earning less than 20,000 = 40 − 15 = 25 men.
The fraction of men earning less than 20,000 is:
Fraction = 25/40 = 5 / 8
Thus, the correct answer is A: 5/8

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?

Heena Khan answered
Yes answer is (b) bcz after dividing the 4200 among all the partners their profits are 1400,1600,1200.and after adding 200 in all's profits their profits will be 1600,1800,1400.and so new ratio will be 8:9:7

 In an election contested by two parties A and B, party A secured 25 percent of the total votes more than Party B. If party B gets 15000 votes. By how much votes does party B loses the election?
  • a)
    8000
  • b)
    10000
  • c)
    12000
  • d)
    15000
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Answer – b) 10000 Explanation : Let total votes = T and party B gets 15000 votes then party A will get T -15000 votes T – 15000 – 15000 = 25T/100
T = 40000, so A get 25000 and B gets 15000 votes, so difference = 10000

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 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.

Alisha goes to a supermarket and bought things worth rupees 60, out of which 40 paise went on sales tax. If the tax rate is 10 percent, then what was the cost of tax free items?
  • a)
    54.60
  • b)
    55.60
  • c)
    56.60
  • d)
    57.60
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Total cost of items = ₹60.
Sales tax paid = 40 paise = ₹0.40.
Tax rate = 10%. So, the tax amount is 10% of the cost of taxed items (denoted as T).
The sales tax equation is:

Solving for T:
Now, the cost of tax-free items is:
Cost of tax-free items = 60 − T − Sales tax = 60 − 4 − 0.40 = 55.60 rupees.
Thus, the cost of tax-free items is ₹55.60.

Monthly salary of A is 30% more than B’s monthly salary and B’s monthly salary is 20% less than C’s. If the difference between the monthly salaries of A and C is Rs 800, then find the annual salary of B.
  • a)
    Rs 14,500
  • b)
    Rs 16,800
  • c)
    Rs 15,000
  • d)
    Rs 16,000
  • e)
    None of these
Correct answer is option 'E'. Can you explain this answer?

Anaya Patel answered
E) None of these Explanation: Let C’s monthly salary = Rs 100, then B’s = (100-20)% of 100 = 80, and A’s monthly = (100+30)% * 80 = 104
If difference between A and C’s monthly salary is Rs 4 then B’s monthly salary is Rs 80
So if difference is Rs 800, B’s monthly salary is (80/4) * 800 = 16,000 So annual salary = 12*16,000

A horse takes 8 steps for every 5 steps of a fox, but 6 steps of a fox are equal to the 3 steps of the horse. What is the ratio of the speed of horse to the fox ?
  • a)
    16:5
  • b)
    20:19
  • c)
    18:23
  • d)
    17:21
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Given:
- A horse takes 8 steps for every 5 steps of a fox.
- 6 steps of a fox are equal to the 3 steps of the horse.

To find: Ratio of the speed of horse to the fox.

Solution:
Let's assume that the horse takes 8 steps in time 't' and the fox takes 5 steps in the same time 't'.
Then, the speed of the horse is 8/t and the speed of the fox is 5/t.

Now, we know that 6 steps of a fox are equal to the 3 steps of the horse.
So, in the same time 't', the fox takes 6/5 of its steps and the horse takes 3/8 of its steps.
Therefore, we can equate their distances covered in time 't':

(5/t) x (6/5) = (8/t) x (3/8)

Simplifying this equation, we get:

6 = 6

This means that the distances covered by both the horse and the fox are equal in the same time 't'.

Therefore, we can say that the speed of the horse is proportional to 8 and the speed of the fox is proportional to 5.
So, the ratio of the speed of horse to the fox is:

8:5

Multiplying both sides by 5, we get:

40:25

Simplifying this ratio, we get:

16:5

Hence, the correct answer is option (A).

Final Answer: Option (A) 16:5

In a library 5 percent books are in English, 10 percent of the remaining are in hindi and 15 percent of the remaining are in Sanskrit. The remaining 11628 books are in French. Then find the total number of books in the library.
  • a)
    8000
  • b)
    12000
  • c)
    16000
  • d)
    20000
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Ravi Singh answered
5% of books are in English,
10% of remaining books are in Hindi,
15% of remaining books are  in Sanskrit. 
Remaining books are in french = 11628
Calculation:
Let the total books in the library be 100%
According to question:
5% of books are in English
Remaining books = 100 - 5 = 95%
10% of remaining are in hindi = 10% of 95 = 9.5
Remaining books = 95 - 9.5 = 85.5%
15% of remaining books are in sanskrit = 15% of 85.5 = 12.825%
Remaining books = 85% - 12.825% = 72.675%
According to question:
72.675% = 11628
⇒ 1% = (11628/72.675)
⇒ 100% = (11628/72.675)× 100 = 16000
∴ Required value = 16000

When the price of rice is increased by 30 percent, a family reduces its consumption such that the expenditure is only 20 percent more than before. If 50 kg of rice is consumed by family before, then find the new consumption of family (approx.)
  • a)
    43kg
  • b)
    44kg
  • c)
    45kg
  • d)
    46kg
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Answer – 4.46kg Explanation : Suppose initially price per kg of rice is 100 then their expenditure is 5000.
Now their expenditure is only increased by only 20% i.e – 6000.
Increased price of rice = 130.
So new consumption = 6000/130 = 46.1

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