AAO Exam-CT 3: Quant (Percentage)

AAO Exam-CT 3- Quant (Percentage)

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AAO Exam-CT 3: Quant (Percentage)
1. In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election ?
  • 62000
  • 52000
  • 59000
  • 60000
  • 65000

Given:

Percentage of candidates voted for candidate A = 30%

Percentage of the candidates voted for candidate B = 60% of the remaining

Difference between those who voted for candidate A and those who didn't vote = 1200

Calculation:

Let the number of persons eligible to vote be x.

Then, voters who voted for A = 30% of x.

Voters who voted for B = 60% of (70% of x).

⇒  of x

⇒ 42% of x.

Voters who did not vote = [100 – (30 + 42)]% of x = 28% of x

⇒ 30% of x – 28% of x = 1200

⇒ 2% of x= 1200

⇒  x = 60000

∴ The total number of voters are 60000

2. Students of class 10th are divided into three sections A, B, And C. The difference between the number of students in sections A and C is 40. If 16.66% of class 10th students are in section A and 60% of the remaining students are in section B, then Find 40% of the total number of students in section B.

  • 32
  • 48
  • 40
  • 58
  • None of the above

Given:

16.66% of class 10th students are in section A.

60% of the remaining students are in section B.

The difference between students in sections A and C is 40.

Calculation:

Let's assume the total number of students in class 10th = 6x.

Then students in section A = 1/6 × 6x 

⇒ x 

Remaining students = 6x - x

⇒ 5x

And students in section B = 3/5 × 5x

⇒ 3x

Students in section C = 6x - 4x

⇒  2x

Now

⇒ 2x - x = 40 

⇒ x = 40

Students in section B = 40 × 3 = 120

Now 40/100 × 120

⇒ 48

3. If the price of an Iphone is reduced by 20% during the festival season, its sale is increased by 80%. If the percentage by which the net sale is increased be m, then what will be the square root of m+5 ? 
  • 7
  • 11
  • 13
  • 17
  • 5

Given:

The price is reduced by 20% and the sale goes up by 80%

Formula used:

% increment = (new value - old value)/old value × 100

Calculation:

Let the price be Rs x per iphone and the no of units sold be y

∴ Sale = Rs x × y

Price of iphone after reduction = x - 20% of x

 x - 20/100 × x

 Rs 4x/5

Number of iphones sold after reduction in price = y + 80% of y

 y + 80/100 × y

 9y/5

∴ Net sale after reduction = Rs (4x/5 × 9y/5)

 Rs 36xy/25

⇒ % increment = (36xy/25 - xy)/xy × 100

 11/25 × 100

 44%

∴ The value of m+5 = 44+5

⇒ m+5 = 49

The square root of m+5 is 7

4. In a committee, 60 people speak English, 30 people speak Hindi and 11 people speak both Hindi and English. Then, how many people speak at least one of these two languages?

  • 79
  • 70
  • 75
  • 72
  • 85

5. Suresh opened his factory in 2003.The production of his factory increases for two consecutive years consistently by 12% and in the third year it decreases by 8%. Again in the next two years it increases by 12% each year and decreases by 8% in the third year. What will be the effect on the production of the Company in 2007?

  • 27%
  • 31%
  • 30%
  • 29%

  • 35%

Given

Increase in production for two consecutive years consistently = 12%

Decrease in production for third year = 8%

Formula used

Percentage = (Value/ total value) × 100

Calculation

Suppose the production of the company in the year 2003 is = x.

Then production of the company in year 2007

⇒ x × 112/100 × 112/100 × 92/100 × 112/100

⇒ 1.29 x

Increase percentage in the production of factory in 2007

⇒ (1.29x – x)/x × 100 

⇒ 29% ∴ The production of the Company in 2007 is increased by 29%.

6. Himanshu decided to donate 25% of his income to a fund for making arrangements for oxygen cylinders to COVID patients. On the day of donation he changed his mind and donated Rs. 4250 which was 85% of what he had decided earlier. How much is Himanshu's income per month?
  • Rs. 21450
  • Rs. 20,000
  • Rs. 30000
  • Rs. 25,000
  • None of these 

Given 

Himanshu donation to fund = Rs. 4250

Formula Used 

Percentage = (Actual/Total) × 100 

Calculation 

Let the Himanshu's income per month be x 

Himanshu donated = 85% of 25% of x 

⇒ 85/100 × 25/100 × x = 4250

⇒ x = 4250 × 100 × 4/85 

x = Rs. 20,000

∴ The Himanshu's income per month is Rs. 20,000

7. The income of Aman is Rs. 30,000 per month and his expenditure is Rs. 20,000 per month. In the next month, his income increases by Rs. 10,000 per month, and expenditure increases to Rs. 25,000 per month. In the next month, his savings increases by what percent?
  • 55%
  • 25%
  • 100%
  • 12.5%
  • None of these

Given:

Previous income of Aman = Rs. 30,000 per month

His previous expenditure = Rs. 20,000 per month

His income increases by Rs. 10,000 per month

His new expenditure = Rs. 25,000 per month

Formula used:

Savings = Income - Expenditure

And Percentage = (Favourable value/Base value) × 100

Calculation:

Previous savings of Aman = His previous income – His previous expenditure

⇒ Rs. 30,000 – Rs. 20,000

⇒ Rs. 10,000

His new income = Rs. 30,000 + Rs. 10,000

And His new savings = His new income – His new expenditure

⇒ Rs. 40,000 – Rs. 25,000

⇒ Rs. 15,000

Increase in savings = Rs. 15,000 – Rs. 10,000 = Rs. 5,000

Now, percentage increase in savings = (Increase in savings/Previous savings) × 100

⇒ (Rs. 5,000/Rs. 10,000) × 100

⇒ (1/2) × 100

⇒ 50%

∴ In next month, the savings of Aman increases by 50%.

8. Total workers in a company in the year 2014 was 1750 and every year there is an increase of 20% and in 2018 there is lay off and the company discharged 25% of the total workers. Calculate the number of workers in the company now.
  • 2350
  • 2345
  • 3458
  • 2268
  • 1890

Given:

Number of workers in 2014 = 1750

Increase% per year = 20%

Percentage of people discharged in 2018 = 25%

Calculation:

Total number of workers in company in the year 2014 = 1750

Total population of the company in the year 2017 = 1750 × (120/100)3

⇒ 3024

Total number of employees in the year 2018 = 3024 × (75/100) = 2268

∴ The total number of employees at present is 2268

9. Rajveer distributed as amount among his 3 sons. Vivek being the eldest brother receives 40% of the amount and the remaining amount is distributed between Vijay and Ramesh in the ratio 5 ∶ 4. If the difference between the amount received by Vivek and Ramesh is Rs.2000. What is the amount which Rajveer distributed?
  • Rs.20,000
  • Rs.16,000
  • Rs.15,000
  • Rs.25,000
  • None of these

Let the amount which Rajveer distributed be x

∴ Amount received by Vivek = (40/100) × 100x = 40x

Remaining amount = 100x – 40x = 60x

Remaining amount is distributed between Vijay and Ramesh in the ratio 5 ∶ 4

⇒ Amount received by Vijay = (5/9) × 60x = 100x/3

Amount received by Ramesh = (4/9) × 60x = 80x/3

The difference between the amount received by Vivek and Ramesh is Rs.2000

∴ 40x – 80x/3 = 2000

⇒ 40x = 6000

⇒ x = 150

∴ Amount distributed by Rajveer = 150 × 100 = Rs.15000

10. Two numbers is in the ratio 8 ∶ 9, when 12.5% of the first number and 11.11% of the second number is added the result will be 200. Calculate 30% of the sum of both the numbers.
  • 900
  • 860
  • 1700
  • 560
  • 510

Given:

Two numbers is in the ratio 8 ∶ 9

If 12.5% of the first number and 11.11% of the second number is added the result will be 2/17 times the sum of both the numbers.

Calculation:

∴ Let the number be 8x and 9x respectively 

According to question,

⇒ 12.5% of 8x + 11.11% of 9x = 200

⇒ 8x/8 + 9x/9 = 200     ----(∵ 12.5% = 1/8, 11.11% = 1/9)

⇒ 2x = 200

⇒ x = 100

∴ Sum of the two numbers = 8 × 100 + 9 × 100 = 1700

30% of the sum of both the numbers

⇒ (30/100) × 1700 = 510

∴ 30% of the sum of both the numbers is 510.

Additional Information

1/8 = 12.5%

1/9 = 11.11% 

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