Numerical Ability Test - 20

Given:

Mita's income is 125% more than that of Sita.

Formula used:

If Mita's income is 125% more than Sita's, then Mita's income is 225% of Sita's income.

Let Sita's income be S .

Then, Mita's income = 225% of S

Calculations:

Let Sita's income = 100

Then, Mita's income = 225

We need to find the percentage by which Sita's income is less than Mita's.

Difference in income = 225 - 100 = 125

Given:

A 20% reduction in the price of an apple enables a man to buy 10 apples more for ₹54.

Formula used:

Let the original price of an apple be ₹x.

After a 20% reduction, the new price = x - 0.2x = 0.8x

Let the original number of apples be n.

Given: 54 = n × x and 54 = (n+10) × 0.8x

Calculations:

54 = n × x

⇒ n = 54/x

54 = (54/x + 10) × 0.8x

⇒ 54 = 43.2 + 8x

⇒ 54 - 43.2 = 8x

⇒ 10.8 = 8x

⇒ x = 1.35

Reduced price per apple = 0.8 × 1.35 = 1.08

Reduced price per dozen = 1.08 × 12 = 12.96

∴ The correct answer is option 2.

Given:

In an examination, a student who gets 20% of the maximum marks fails by 5 marks.

Another student who scores 30% of the maximum marks, gets 20 marks more than the passing marks.

Formula used:

Let the maximum marks be M and the passing marks be P.

20% of M = P - 5

30% of M = P + 20

Calculation:

0.20M = P - 5

0.30M = P + 20

Solving these two equations:

⇒ 0.30M - 0.20M = (P + 20) - (P - 5)

⇒ 0.10M = 25

⇒ M = 250

Now substituting M back into the first equation:

0.20 × 250 = P - 5

⇒ 50 = P - 5

⇒ P = 55

Percentage required for passing = (P / M) × 100

⇒ (55 / 250) × 100 = 22%

∴ The correct answer is option 1.

Given:

The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10,000, the present population is?

Concept:

To find the present population after a decrease over a period, we use the formula for compound percentage decrease.

Formula Used:

Present Population = P × (1 - r/100)ⁿ

where P is the initial population, r is the rate of decrease, and n is the number of years.

Calculation:

We have,

⇒ P = 10,000, r = 20%, n = 2

⇒ Present Population = 10,000 × (1 - 20/100)²

⇒ Present Population = 10,000 × (0.80)²

⇒ Present Population = 10,000 × 0.64

⇒ Present Population = 6,400

∴ The present population is 6,400.

Given:

Length in meters = 3 m.

Length in centimeters = 75 cm.

Formula Used:

Percentage = (Part/Whole) × 100

Calculation:

Convert 3 meters to centimeters:

3 meters = 3 × 100 = 300 cm

Percentage = (75 / 300) × 100

⇒ Percentage = 0.25 × 100

⇒ Percentage = 25%

The percentage of 3 meters that is 75 cm is 25%.

Given:

Terlin scores 65 marks out of 80 in French, 75 marks out of 100 in English, 45 marks out of 70 in Spanish, and 25 marks out of 50 in Japanese.

Concept:

To calculate the total percentage marks obtained by a student, we sum the marks obtained in all subjects and divide it by the sum of the total marks of all subjects. Then, multiply it by 100 to get the percentage.

Formula Used:

Total Percentage = (Marks Obtained / Total Marks) × 100

Calculation:

We have,

⇒ Marks Obtained in French = 65, Total Marks = 80

⇒ Marks Obtained in English = 75, Total Marks = 100

⇒ Marks Obtained in Spanish = 45, Total Marks = 70

⇒ Marks Obtained in Japanese = 25, Total Marks = 50

Sum of Marks Obtained:

⇒ 65 + 75 + 45 + 25 = 210

Sum of Total Marks:

⇒ 80 + 100 + 70 + 50 = 300

Calculation of Total Percentage:

⇒ (210 / 300) × 100

⇒ 0.7 × 100

⇒ 70%

∴ Total Percentage Obtained by Turlin It is 70%.

Given:

Two-fifths of one-third of three-sevenths of a number is 15.

Formula Used:

Let the number be x .

Given:

If the price of tea is increased by 40%, by what percentage must the consumption of tea be decreased so as not to increase the expenditure?

Formula used:

Let the original price be ₹100 and the new price be ₹140 (increased by 40%).

Expenditure = Price × Consumption

To keep the expenditure same:

100 × Original Consumption = 140 × New Consumption

Calculation:

Let Original Consumption = 1 unit.

100 × 1 = 140 × New Consumption

⇒ New Consumption = 100/140

⇒ New Consumption = 5/7

Decrease in Consumption = 1 - (5/7)

⇒ Decrease in Consumption = (2/7)

Percentage Decrease = (2/7) × 100

Given:

After a 9% increase in salary, a person received Rs. 6,300.

Formula Used:

New Salary = Original Salary × (1 + Percentage Increase)

Calculation:

Let the original salary be x. After a 9% increase, the salary becomes:

New Salary = x × (1 + 0.09)

New Salary = x × 1.09

According to the question:

1.09 × x = 6300

⇒ x = 6300 / 1.09

⇒ x ≈ 5779

The salary before the increase was Rs. 5,779.

Given:

A is 25% more than B and B is 30% less than C. If C is 20% more than D, then by what percentage is A more than D?

Formula Used:

A = B + 25% of B

B = C - 30% of C

C = D + 20% of D

Calculation:

Let D = 100

⇒ C = 100 + 20% of 100

⇒ C = 100 + 20

⇒ C = 120

⇒ B = 120 - 30% of 120

⇒ B = 120 - 36

⇒ B = 84

⇒ A = 84 + 25% of 84

⇒ A = 84 + 21

⇒ A = 105

Percentage by which A is more than D:

⇒ (A - D)/(D) × 100

⇒ (105 - 100)/(100) × 100

⇒ (5)/(100) × 100

⇒ 5%

∴ The correct answer is option (1).