Numerical Ability Test - 19

Given:

List price of the article = ₹250

Successive discounts = 12% and 16%

Transportation cost = 10% of the cost price

Desired profit = 25%

Formula Used:

1. Cost price after successive discounts = List price × (1 - Discount₁) × (1 - Discount₂)

2. Total cost price = Cost price after discounts + Transportation cost

3. Selling price = Total cost price × (1 + Profit percentage)

Calculation:

Cost price after first discount = ₹250 × (1 - 12/100)

⇒ ₹250 × 0.88 = ₹220

Cost price after second discount = ₹220 × (1 - 16/100)

⇒ ₹220 × 0.84 = ₹184.80

Transportation cost = 10% of ₹184.80

⇒ 0.10 × ₹184.80 = ₹18.48

Total cost price = ₹184.80 + ₹18.48

⇒ ₹203.28

Selling price for 25% profit = ₹203.28 × (1 + 25/100)

⇒ ₹203.28 × 1.25

⇒ ₹254.10

The price at which the dealer should sell the article to earn a profit of 25% is ₹254.10.

Given:

The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%.

Formula used:

Resultant Price = Initial Price × (1 + Increase%) × (1 - Decrease%) × (1 + Increase%)

Calculation:

Let the initial price be 100 units.

After 25% increase:

Price = 100 × (1 + 0.25)

⇒ Price = 100 × 1.25 = 125 units

After 20% decrease:

Price = 125 × (1 - 0.20)

⇒ Price = 125 × 0.80 = 100 units

After 10% increase:

Price = 100 × (1 + 0.10)

⇒ Price = 100 × 1.10 = 110 units

Resultant Increase = 110 - 100 = 10 units

Resultant Increase % = (10 / 100) × 100 = 10%

∴ The correct answer is option 4.

Given:

Selling price at loss (SP₁) = ₹460

Selling price at profit (SP₂) = ₹580

Profit = 2 × Loss

Formula used:

Loss = Cost Price (CP) - SP₁

Profit = SP₂ - CP

Profit = 2 × Loss

Calculation:

Let CP = x

Loss = x - 460

Profit = 580 - x

⇒ 580 - x = 2 × (x - 460)

⇒ 580 - x = 2x - 920

⇒ 580 + 920 = 3x

⇒ 1500 = 3x

⇒ x = 500

∴ The correct answer is option (2).

Given:

A house and a shop were sold for ₹1 lakh each.

House sale resulted in 20% Loss.

Shop sale resulted in 20% Profit.

Formula used:

Loss = Cost Price - Selling Price

Profit = Selling Price - Cost Price

Calculation:

Let the Cost Price (CP) of the house be H, and for the shop be S.

House:

Selling Price (SP) = ₹1,00,000

Loss = 20% of CP

⇒ ₹1,00,000 = H - 0.2H

⇒ ₹1,00,000 = 0.8H

⇒ H = ₹1,00,000 / 0.8

⇒ H = ₹1,25,000

Shop:

Selling Price (SP) = ₹1,00,000

Profit = 20% of CP

⇒ ₹1,00,000 = S + 0.2S

⇒ ₹1,00,000 = 1.2S

⇒ S = ₹1,00,000 / 1.2

⇒ S = ₹83,333.33

Total Cost Price (CP) = H + S

⇒ Total CP = ₹1,25,000 + ₹83,333.33

⇒ Total CP = ₹2,08,333.33

Total Selling Price (SP) = ₹1,00,000 + ₹1,00,000

⇒ Total SP = ₹2,00,000

Net Loss = Total CP - Total SP

⇒ Net Loss = ₹2,08,333.33 - ₹2,00,000

⇒ Net Loss = ₹8,333.33

Net Loss in Lakh = ₹8,333.33 / 1,00,000

⇒ Net Loss = 0.083333 Lakh

⇒ Net Loss = 1/12 Lakh

∴ The correct answer is option (3).

Given:

If the cost price of 30 tables is equal to the selling price of 40 tables, then what is the loss percentage?

Formula used:

⇒ Loss % = 25%

∴ The correct answer is option 1.

Given:

Scheme 1: 2 successive discounts of 5% and 5%

Scheme 2: Single discount of 10%

Scheme 3: 2 successive discounts of 8% and 2%

Formula used:

Successive discount formula: (1 - d1) × (1 - d2)

Calculations:

Scheme 1:

⇒ (1 - 0.05) × (1 - 0.05)

⇒ 0.95 × 0.95

⇒ 0.9025

⇒ Effective discount = 1 - 0.9025 = 0.0975 or 9.75%

Scheme 2:

⇒ Single discount = 10%

Scheme 3:

⇒ (1 - 0.08) × (1 - 0.02)

⇒ 0.92 × 0.98

⇒ 0.9016

⇒ Effective discount = 1 - 0.9016 = 0.0984 or 9.84%

Given:

Cost Price (CP) = Rs. 10,000

Selling Price (SP) = Rs. 12,000

Potential Selling Price = Rs. 13,000

Calculation:

Potential Profit = Potential Selling Price - Cost Price

Potential Profit = Rs. 13,000 - Rs. 10,000

Potential Profit = Rs. 3,000

Actual Profit = Selling Price - Cost Price

Actual Profit = Rs. 12,000 - Rs. 10,000

Actual Profit = Rs. 2,000

Loss = 3000 - 2000 = 1000 

In percentage = (1000/10000)× 100 

⇒ 10% loss

∴ The percentage loss that he incurs is 10%.

Given:

Loss% (a) = 25%

Less weight (b) = 45%

Formula Used:

Profit% / Loss% = (b ± a) / (100 - b) × 100

Calculations:

As, a = 25% and b = 45%

Then,

⇒ Profit% / Loss% = (b ± a) / (100 - b) × 100

⇒ (45 - 25) / (100 - 45) × 100

⇒ 20 / 55 × 100

Given:

Selling price of 100 pens = Cost price of 140 pens

Concept:

To find the profit percentage, we need to determine the cost price (CP) and selling price (SP) for one pen and then use the profit percentage formula.

Formula Used:

Profit Percentage = ((SP - CP) / CP) × 100%

Calculation:

Let the cost price of one pen be CP.

Then, the cost price of 140 pens = 140 × CP

Given that the selling price of 100 pens is equal to the cost price of 140 pens,

⇒ Selling price of 100 pens = 140 × CP

⇒ Selling price of one pen = (140 × CP) / 100

⇒ Selling price of one pen = 1.4 × CP

Now, we calculate the profit percentage:

⇒ Profit Percentage = ((1.4 × CP - CP) / CP) × 100%

⇒ Profit Percentage = (0.4 × CP / CP) × 100%

⇒ Profit Percentage = 0.4 × 100%

⇒ Profit Percentage = 40%

∴ The correct answer is option 3.

Given:

Selling price of each refrigerator = Rs. 10,000

Loss on one refrigerator = 20%

Gain on the other refrigerator = 20%

Formula Used:

Loss Percentage = [(Cost Price - Selling Price)/Cost Price] × 100

Gain Percentage = [(Selling Price - Cost Price)/Cost Price] × 100

Calculation:

Let the cost price of the first refrigerator be C1.

Loss of 20% means 10,000 = C1 - 0.2C1

⇒ 10,000 = 0.8C1

⇒ C1 = 10,000/0.8

⇒ C1 = 12,500

Let the cost price of the second refrigerator be C2.

Gain of 20% means 10,000 = C2 + 0.2C2

⇒ 10,000 = 1.2C2

⇒ C2 = 10,000/1.2

⇒ C2 = 8,333.33

Total cost price = C1 + C2 = 12,500 + 8,333.33 = 20,833.33

Total selling price = 10,000 + 10,000 = 20,000

Loss = Total cost price - Total selling price

Loss = 20,833.33 - 20,000 = 833.33

Loss Percentage = (833.33/20,833.33) × 100

⇒ Loss Percentage = 4%

The merchant incurred a loss of 4% on the whole transaction.