Consumption and Expenditure MCQ Quiz - Objective Question with Answer for Consumption and Expenditure - Download Free PDF

Given:

A number is first increased by 12%, and the increased number is decreased by 8%.

Formula used:

Net change percentage = \((x + y + \frac{xy}{100})\)

Where,

x = Percentage increase = 12%

y = Percentage decrease = -8% (negative because it’s a decrease)

Calculations:

Net change percentage = \((x + y + \frac{xy}{100})\)

⇒ Net change percentage = \((12 + (-8) + \frac{12 × (-8)}{100})\)

⇒ Net change percentage = \((12 - 8 - \frac{96}{100})\)

⇒ Net change percentage = \((4 - 0.96)\)

⇒ Net change percentage = 3.04%

∴ The net change is a 3.04% increase, and the correct answer is option (1).

Formula used:

Percentage Reduction in Consumption = \(\dfrac{\text{Initial Consumption - Reduced Consumption}}{\text{Initial Consumption}} \times 100\)

Calculation:

Let the initial price of petrol be ₹100 and consumption be 100 litres.

Initial expenditure = Price × Consumption

Let the reduced consumption be x litres.

New expenditure = New Price × Reduced Consumption

New expenditure = 114% of Initial expenditure

Initial expenditure = 100 × 100 = ₹10,000

New price = 100 + 50 = ₹150 per litre

New expenditure = ₹10,000 × \(\dfrac{114}{100}\) = ₹11,400

New expenditure = New Price × Reduced Consumption

⇒ ₹11,400 = ₹150 × x

⇒ x = \(\dfrac{11400}{150}\) = 76 litres

Percentage reduction in consumption:

⇒ \(\dfrac{100 - 76}{100} \times 100\)

⇒ \(\dfrac{24}{100} \times 100\)

⇒ 24%

∴ The correct answer is option (2).

Given:

Expenditure increase = 19%

Formula used:

Initial expenditure = Initial price × Initial consumption

Final expenditure = Price after increase × Reduced consumption

Final expenditure = 1.19 × Initial expenditure

Calculation:

Let the Initial price of petrol = ₹100

Price after increase = ₹140 (40% increase)

Let initial consumption = 100 litres

Initial expenditure = 100 × 100 = ₹10,000

Final expenditure = 1.19 × ₹10,000 = ₹11,900

⇒ 140 × x = 11,900

⇒ x = 85 litres

Reduction in consumption = Initial consumption - Reduced consumption

⇒ Reduction = 100 - 85 = 15 litres

Reduction percentage = (Reduction ÷ Initial consumption) × 100

⇒ Reduction percentage = (15 ÷ 100) × 100 = 15%

∴ The correct answer is option (2).

Given:

Price of sugar is raised by 20%.

Formula Used:

Percentage reduction in consumption = (Percentage increase in price) / (1 + Percentage increase in price)

Calculation:

Percentage increase in price = 20%

Let the original price be 100 units, then the new price = 100 + 20 = 120 units

Let the original consumption be 100 units.

To keep the expenditure same:

Original expenditure = New expenditure

⇒ 100 × 100 = 120 × New consumption

⇒ New consumption = (100 × 100) / 120

⇒ New consumption = 10000 / 120

⇒ New consumption = 83.33 units

Percentage reduction in consumption = (Original consumption - New consumption) / Original consumption × 100

⇒ Percentage reduction in consumption = (100 - 83.33) / 100 × 100

⇒ Percentage reduction in consumption = 16.67%

The householder must reduce his consumption by 16.67% to not increase the expenditure.

Given:

The price of sugar decreases by 20%.

Formula Used:

To keep the expenditure unchanged: (Original Price × Original Quantity) = (New Price × New Quantity)

Calculation:

Let the original price be P and the original quantity be Q.

New Price = P - 0.20P = 0.80P

Let increase consumption of sugar = x%

New Quantity = Q + x% of Q = Q(1 + x/100)

Expenditure remains unchanged:

PQ = 0.80P × Q(1 + x/100)

⇒ Q = 0.80Q(1 + x/100)

⇒ 1 = 0.80(1 + x/100)

⇒ 1 = 0.80 + 0.80x/100

⇒ 1 - 0.80 = 0.80x/100

⇒ 0.20 = 0.80x/100

⇒ x = (0.20 × 100) / 0.80

⇒ x = 25%

The householder must increase her consumption of sugar by 25% to keep the expenditure unchanged.

Given:

The reduction of 20% in the price of rice enables a person to obtain 50 kg more for Rs. 450.

Concept used:

Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let's suppose, originally for Rs. 450, one could get Q kg rice.

Now, for Rs. 450, one can get (Q + 50) kg rice.

​According to the question,

\(\frac {450}{Q} × (1 - 20\%) = \frac {450}{Q + 50}\)

⇒ \(\frac {1}{Q} × 0.8 = \frac {1}{Q + 50}\)

⇒ \(\frac {1}{Q} × \frac {4}{5} = \frac {1}{Q + 50}\)

⇒ 4Q + 200 = 5Q

⇒ Q = 200

Now, the original price of rice (per kg) = 450/200 = Rs. 2.25

∴ The original price of rice per kg is Rs. 2.25.

Shortcut Trick

​We know, 20% = 1/5,

Consumption difference (5 - 4) = 1 unit → 50 kg

Then, 4 unit → 50 × 4 = 200 kg

Now, price of 200 kg is 450

Then price of 1 kg is 450/200 = Rs.2.25

Given:-

The price of oil is increased by 81%

Calculation:-

Let initially oil is consumed 100lt at 100₹/lt.

Initial expenditure = 100 × 100 = 10000

Now, new price = 181% of 100 = ₹181 And

Required percentage = [{(181) - 100}/181] × 100 = % = 44.75% 

 ∴ The required answer is 44.75.

Alternate Method

               Price          Consumption          Expenditure

Old          100               181                         a

New         181               100                        a

percentage change = (81/181) * 100 = 44.75

 ∴ The required answer is 44.75.

Given : 

Price of petrol increased by 7%.

Formula Used : 

Expenditure = Price × Consumtion

Calculation : 

Price of petrol increased by 7%

So,

Percentage decrease in consumption = 7/107 × 100

⇒ \( 6 \frac{58}{107} \% \)

∴ The correct answer is  \( 6 \frac{58}{107} \% \).

Given:

The price of petrol is increased by 28%

Calculation:

Let the price of petrol before the increase be Rs. 100a per 1000 ml

New price = 100a × 128%

⇒ Rs. 128a

Now,

If the consumer wants to maintain the expenditure as before he will still buy petrol for Rs. 100a

Now,

In Rs. 100a he will get = (1000/128a) × 100a

⇒ 781.25 ml

Consumption decrease = 1000 ml - 781.25 ml

⇒ 218.75

% decrease = (218.75/1000) × 100

⇒ 21.875 ≈ 21.88%

∴ The required answer is 21.88%.

Formula used:

Percentage Reduction in Consumption = \(\dfrac{\text{Initial Consumption - Reduced Consumption}}{\text{Initial Consumption}} \times 100\)

Calculation:

Let the initial price of petrol be ₹100 and consumption be 100 litres.

Initial expenditure = Price × Consumption

Let the reduced consumption be x litres.

New expenditure = New Price × Reduced Consumption

New expenditure = 114% of Initial expenditure

Initial expenditure = 100 × 100 = ₹10,000

New price = 100 + 50 = ₹150 per litre

New expenditure = ₹10,000 × \(\dfrac{114}{100}\) = ₹11,400

New expenditure = New Price × Reduced Consumption

⇒ ₹11,400 = ₹150 × x

⇒ x = \(\dfrac{11400}{150}\) = 76 litres

Percentage reduction in consumption:

⇒ \(\dfrac{100 - 76}{100} \times 100\)

⇒ \(\dfrac{24}{100} \times 100\)

⇒ 24%

∴ The correct answer is option (2).

Given:

The price of sugar decreases by 20%.

Formula Used:

To keep the expenditure unchanged: (Original Price × Original Quantity) = (New Price × New Quantity)

Calculation:

Let the original price be P and the original quantity be Q.

New Price = P - 0.20P = 0.80P

Let increase consumption of sugar = x%

New Quantity = Q + x% of Q = Q(1 + x/100)

Expenditure remains unchanged:

PQ = 0.80P × Q(1 + x/100)

⇒ Q = 0.80Q(1 + x/100)

⇒ 1 = 0.80(1 + x/100)

⇒ 1 = 0.80 + 0.80x/100

⇒ 1 - 0.80 = 0.80x/100

⇒ 0.20 = 0.80x/100

⇒ x = (0.20 × 100) / 0.80

⇒ x = 25%

The householder must increase her consumption of sugar by 25% to keep the expenditure unchanged.

Given:

Original total cost = Rs. 120

Reduction in price = 6.25%

Extra sugar bought = 1 kg

Formula Used:

Reduced price per kg = (Original price per kg) × (1 - Reduction percentage)

Calculation:

Let the original price per kg be Rs. x.

Reduction percentage = 6.25% = 6.25/100 = 1/16

Reduced price per kg = x × (1 - 1/16) = 15x/16

With the reduced price, the man can buy 1 kg more for Rs. 120.

120 / (15x/16) - 120 / x = 1

120 × (16/15x) - 120 / x = 1

⇒ 1280 / 15x - 120 / x = 1

⇒ 1280 - 1800 / 15x = 1

⇒ (1280 - 1800) / 15x = 1

⇒ -520 / 15x = 1

⇒ 15x = 520

⇒ x = 520 / 15

⇒ x = 34.67

Reduced price per kg = 15x/16

⇒ 15 × 34.67 / 16

⇒ 520 / 16

⇒ Rs. 7.5

The reduced price per kg of sugar is Rs. 7.5.

Given:

A number is first increased by 12%, and the increased number is decreased by 8%.

Formula used:

Net change percentage = \((x + y + \frac{xy}{100})\)

Where,

x = Percentage increase = 12%

y = Percentage decrease = -8% (negative because it’s a decrease)

Calculations:

Net change percentage = \((x + y + \frac{xy}{100})\)

⇒ Net change percentage = \((12 + (-8) + \frac{12 × (-8)}{100})\)

⇒ Net change percentage = \((12 - 8 - \frac{96}{100})\)

⇒ Net change percentage = \((4 - 0.96)\)

⇒ Net change percentage = 3.04%

∴ The net change is a 3.04% increase, and the correct answer is option (1).

Given:

The reduction of 20% in the price of rice enables a person to obtain 50 kg more for Rs. 450.

Concept used:

Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let's suppose, originally for Rs. 450, one could get Q kg rice.

Now, for Rs. 450, one can get (Q + 50) kg rice.

​According to the question,

\(\frac {450}{Q} × (1 - 20\%) = \frac {450}{Q + 50}\)

⇒ \(\frac {1}{Q} × 0.8 = \frac {1}{Q + 50}\)

⇒ \(\frac {1}{Q} × \frac {4}{5} = \frac {1}{Q + 50}\)

⇒ 4Q + 200 = 5Q

⇒ Q = 200

Now, the original price of rice (per kg) = 450/200 = Rs. 2.25

∴ The original price of rice per kg is Rs. 2.25.

Shortcut Trick

​We know, 20% = 1/5,

Consumption difference (5 - 4) = 1 unit → 50 kg

Then, 4 unit → 50 × 4 = 200 kg

Now, price of 200 kg is 450

Then price of 1 kg is 450/200 = Rs.2.25

Given:-

The price of oil is increased by 81%

Calculation:-

Let initially oil is consumed 100lt at 100₹/lt.

Initial expenditure = 100 × 100 = 10000

Now, new price = 181% of 100 = ₹181 And

Required percentage = [{(181) - 100}/181] × 100 = % = 44.75% 

 ∴ The required answer is 44.75.

Alternate Method

               Price          Consumption          Expenditure

Old          100               181                         a

New         181               100                        a

percentage change = (81/181) * 100 = 44.75

 ∴ The required answer is 44.75.