Two Percentage MCQ Quiz - Objective Question with Answer for Two Percentage - Download Free PDF

Given:

Initial Salary = \(S\)

First increase = 20%

Then decrease = 20%

Formula Used:

Final Salary = Initial Salary × (1 + Increase%) × (1 - Decrease%)

Calculation:

Initial Salary = \(S\)

After 20% increase:

\(S_{\text{new}} = S × (1 + \frac{20}{100})\)

\(S_{\text{new}} = S × 1.20\)

After 20% decrease on new salary:

\(S_{\text{final}} = S_{\text{new}} × (1 - \frac{20}{100})\)

\(S_{\text{final}} = S × 1.20 × 0.80\)

\(S_{\text{final}} = S × 0.96\)

Change in Salary = Final Salary - Initial Salary

Change in Salary = \(S × 0.96 - S\)

Change in Salary = \(S(0.96 - 1)\)

Change in Salary = \(S(-0.04)\)

Percentage change in Salary = \(\frac{-0.04S}{S} × 100\)

Percentage change in Salary = -4%

The correct answer is option 1: 4% decreased.

Given:

The cost of apples is increased by 20% and then decreased by 20%.

Calculation:

Let the price of apples be Rs. 100

After increase it is 100 × 120%

⇒ Rs. 120

After decrease it is 120 × 80%

⇒ Rs. 96

So, decrease = 100 - 96

⇒ Rs. 4

% of decrease = (4/100) × 100

⇒ 4%

∴ The net percentage decrease is 4%.

Shortcut Trick

Given:

The cost of apples is increased by 20% and then decreased by 20%.

Calculation:

Let the price of apples be Rs. 100

After increase it is 100 × 120%

⇒ Rs. 120

After decrease it is 120 × 80%

⇒ Rs. 96

So, decrease = 100 - 96

⇒ Rs. 4

% of decrease = (4/100) × 100

⇒ 4%

∴ The net percentage decrease is 4%.

Shortcut Trick

Given:

Initial Salary = \(S\)

First increase = 20%

Then decrease = 20%

Formula Used:

Final Salary = Initial Salary × (1 + Increase%) × (1 - Decrease%)

Calculation:

Initial Salary = \(S\)

After 20% increase:

\(S_{\text{new}} = S × (1 + \frac{20}{100})\)

\(S_{\text{new}} = S × 1.20\)

After 20% decrease on new salary:

\(S_{\text{final}} = S_{\text{new}} × (1 - \frac{20}{100})\)

\(S_{\text{final}} = S × 1.20 × 0.80\)

\(S_{\text{final}} = S × 0.96\)

Change in Salary = Final Salary - Initial Salary

Change in Salary = \(S × 0.96 - S\)

Change in Salary = \(S(0.96 - 1)\)

Change in Salary = \(S(-0.04)\)

Percentage change in Salary = \(\frac{-0.04S}{S} × 100\)

Percentage change in Salary = -4%

The correct answer is option 1: 4% decreased.

Given:

The cost of apples is increased by 20% and then decreased by 20%.

Calculation:

Let the price of apples be Rs. 100

After increase it is 100 × 120%

⇒ Rs. 120

After decrease it is 120 × 80%

⇒ Rs. 96

So, decrease = 100 - 96

⇒ Rs. 4

% of decrease = (4/100) × 100

⇒ 4%

∴ The net percentage decrease is 4%.

Shortcut Trick

Given:

Initial Salary = \(S\)

First increase = 20%

Then decrease = 20%

Formula Used:

Final Salary = Initial Salary × (1 + Increase%) × (1 - Decrease%)

Calculation:

Initial Salary = \(S\)

After 20% increase:

\(S_{\text{new}} = S × (1 + \frac{20}{100})\)

\(S_{\text{new}} = S × 1.20\)

After 20% decrease on new salary:

\(S_{\text{final}} = S_{\text{new}} × (1 - \frac{20}{100})\)

\(S_{\text{final}} = S × 1.20 × 0.80\)

\(S_{\text{final}} = S × 0.96\)

Change in Salary = Final Salary - Initial Salary

Change in Salary = \(S × 0.96 - S\)

Change in Salary = \(S(0.96 - 1)\)

Change in Salary = \(S(-0.04)\)

Percentage change in Salary = \(\frac{-0.04S}{S} × 100\)

Percentage change in Salary = -4%

The correct answer is option 1: 4% decreased.

Given:

The price of an article was increased by x%. Later the new price was decreased by x%.

Latest price = ₹1

Calculation:

Let the original price be P. After increasing by x%, the price becomes:

P × (1 + x/100)

After decreasing by x%, the new price becomes:

P × (1 + x/100) × (1 - x/100)

We are given that the latest price = ₹1, so:

P × (1 + x/100) × (1 - x/100) = 1

⇒ P × (1 - x²/100²) = 1

⇒ P = 1 / (1 - x²/100²)

⇒ P = 100² / (100² - x²)

⇒ P = ₹(10000) / ((100 + x)(100 - x))

∴ The correct answer is option (1).

Given:

A number was increased by 40% and then decreased by 40%.

Formula used:

Net change percentage = (Increase × Decrease) / 100

Calculation:

Increase = 40%

Decrease = 40%

⇒ Net change percentage = (40 × 40) / 100

⇒ Net change percentage = 1600 / 100

⇒ Net change percentage = 16%

Since the number was decreased after the increase, the net change is a decrease.

∴ The correct answer is option (2): 16% decrease.

Given:

First, number is increased by 30%

Then, the number is decreased by 30%

Formula used:

Net percentage change when two successive changes of \( a\% \) and \( b\% \) are applied:

\( \text{Net % change} = a + b + \dfrac{ab}{100} \)

Calculation:

\( a = +30,\ b = -30 \)

\( \text{Net % change} = 30 - 30 + \dfrac{30 \times (-30)}{100} \)\(= -9\% \)

∴ Net percentage change = 9% decrease