True Discount Questions and Answers

Answer: A

The two schemes differ only in the discount rate, so the shortfall is the extra discount measured on the marked price.

\[ (8\% - 5\%) \times \text{MP} = 45 \]

\[ 0.03 \times \text{MP} = 45 \quad\Longrightarrow\quad \text{MP} = \frac{45}{0.03} = \text{Rs. } 1500 \]

Checking: a 5% discount gives Rs. 1425 and an 8% discount Rs. 1380 - exactly Rs. 45 apart. The cost price never enters the calculation, because it is the same under both schemes and cancels out of the profit difference.

Answer: A

Single 30% discount:

\[ 1000 \times 0.70 = \text{Rs. } 700 \]

Successive 15% and 15%:

\[ 1000 \times 0.85 \times 0.85 = 1000 \times 0.7225 = \text{Rs. } 722.50 \]

\[ \text{difference} = 722.50 - 700 = \text{Rs. } 22.50 \]

The single discount is the better one for the buyer. The gap equals \( 1000 \times 0.15 \times 0.15 = 22.50 \) - the product term that successive discounting always forfeits.

Answer: B

Apply the first discount, then find what fraction of that remains.

\[ 6400 \times (1 - 0.20) = \text{Rs. } 5120 \]

\[ \frac{4608}{5120} = 0.90 \quad\Longrightarrow\quad \text{second discount} = 10\% \]

Checking: \( 5120 \times 0.90 = 4608 \).

The overall reduction is \( \dfrac{6400 - 4608}{6400} = 28\% \), which matches \( 1 - 0.80 \times 0.90 \) - but 28% is the combined figure, not the second discount.

Answer: B

Take the cost price as 100, so the marked price is 120.

\[ \text{SP} = 120 \times (1 - 0.30) = 120 \times 0.70 = 84 \]

\[ \text{loss} = 100 - 84 = 16 \quad\Longrightarrow\quad \text{loss}\% = \frac{16}{100} \times 100 = 16\% \]

Loss percentage is always measured against the cost price, not the marked price. Against the marked price the fall would read \( \tfrac{36}{120} = 30\% \), which is just the discount again.

Answer: D

Let the cost price be 100 and the marked price be \( M \). After a 40% discount the seller must still make 20% profit.

\[ M \times (1 - 0.40) = 100 \times 1.20 \]

\[ 0.6M = 120 \quad\Longrightarrow\quad M = 200 \]

\[ \text{increase over cost price} = \frac{200 - 100}{100} \times 100 = 100\% \]

So the article must be marked at double its cost. Adding 20% and 40% to get 60% is the trap: the discount is taken off the marked price while the profit is measured on the cost price, so the two percentages act on different bases.

Answer: C

Multiply the three retained fractions.

\[ (1-0.10)(1-0.20)(1-0.30) = 0.90 \times 0.80 \times 0.70 \]

\[ 0.90 \times 0.80 = 0.72, \qquad 0.72 \times 0.70 = 0.504 \]

\[ \text{single equivalent discount} = 1 - 0.504 = 0.496 = 49.6\% \]

Adding the rates gives 60%, well above the truth, because each later discount acts on a smaller base. Chaining discounts can never reach 100% however many are applied.

Answer: B

Work forwards from cost to selling price, then backwards from selling price to the advertised (marked) price.

\[ \text{SP} = 900 \times 1.10 = \text{Rs. } 990 \]

The 12% discount is taken off the advertised price, so

\[ \text{MP} \times (1 - 0.12) = 990 \]

\[ \text{MP} = \frac{990}{0.88} = \text{Rs. } 1125 \]

Profit is reckoned on the cost price and discount on the marked price - two different bases, which is why they cannot be netted off against each other.

Answer: C

\[ (1 - 0.15)(1 - 0.10) = 0.85 \times 0.90 = 0.765 \]

\[ \text{single equivalent discount} = 1 - 0.765 = 0.235 = 23.5\% \]

Or by the formula

\[ a + b - \frac{ab}{100} = 15 + 10 - \frac{150}{100} = 23.5\% \]

The naive sum of 25% overstates the discount by exactly the correction term \( \tfrac{ab}{100} = 1.5\% \).

Answer: C

Start from the profit, which is measured on the cost price.

\[ 0.10 \times \text{CP} = 63 \quad\Longrightarrow\quad \text{CP} = \text{Rs. } 630 \]

\[ \text{SP} = 630 + 63 = \text{Rs. } 693 \]

That selling price is the list price after a 23% discount:

\[ \text{LP} \times (1 - 0.23) = 693 \quad\Longrightarrow\quad \text{LP} = \frac{693}{0.77} = \text{Rs. } 900 \]

The chain runs cost → selling price → list price; jumping straight from cost to list price by combining 10% and 23% mixes the two different bases.

Answer: A

A "double discount" applies the second rate to the already-reduced price.

\[ 1000 \times (1 - 0.20) = \text{Rs. } 800 \]

\[ 800 \times (1 - 0.10) = \text{Rs. } 720 \]

The single equivalent discount is

\[ 1 - 0.80 \times 0.90 = 0.28 = 28\% \]

not 30%, so he pays Rs. 720 rather than Rs. 700. Rs. 800 is the price after the first discount only.