True Discount Questions and Answers

Answer: D

Both discounts apply in turn to the price tag, so work backwards from what she paid.

\[ \text{MP} \times 0.75 \times 0.90 = 405 \]

\[ \text{MP} \times 0.675 = 405 \quad\Longrightarrow\quad \text{MP} = \frac{405}{0.675} = \text{Rs. } 600 \]

Checking forwards: \( 600 \times 0.75 = 450 \), and \( 450 \times 0.90 = 405 \). Rs. 450 appears as a distractor because it is the price after the first discount only.

Answer: D

The cash discount applies to the already-reduced price, so multiply the two factors.

\[ 3600 \times (1 - 0.25) = 3600 \times 0.75 = \text{Rs. } 2700 \]

\[ 2700 \times (1 - 0.02) = 2700 \times 0.98 = \text{Rs. } 2646 \]

Adding the rates to 27% would give Rs. 2628 - Rs. 18 too little, because the 2% is charged on Rs. 2700, not on the full Rs. 3600.

Answer: A

The question asks for the single equivalent discount, which comes from multiplying the retained fractions.

\[ (1 - 0.30)(1 - 0.20) = 0.70 \times 0.80 = 0.56 \]

\[ \text{total discount} = 1 - 0.56 = 0.44 = 44\% \]

The bill amount of Rs. 1250 is not needed: the percentage is the same whatever the bill. Adding 30% and 20% gives 50%, which overstates the saving by the product \( 0.30 \times 0.20 = 6\% \).

Answer: B

The card discount is applied after the online discount, so the two factors multiply.

\[ 15000 \times (1 - 0.10) = \text{Rs. } 13500 \]

\[ 13500 \times (1 - 0.05) = 13500 \times 0.95 = \text{Rs. } 12825 \]

Treating the discounts as a combined 15% gives Rs. 12,750 - Rs. 75 less than the true figure, and it is offered as a distractor for exactly that reason. Rs. 13,500 is the price after the online discount alone.

Answer: B

Revenue is price multiplied by volume, so scale each by its own factor.

\[ \text{price factor} = 1 - 0.25 = 0.75, \qquad \text{volume factor} = 1 + 0.40 = 1.40 \]

\[ \text{revenue factor} = 0.75 \times 1.40 = 1.05 \]

\[ \text{change} = 1.05 - 1 = 0.05 = 5\% \text{ increase} \]

Subtracting the percentages (\( 40\% - 25\% = 15\% \)) is wrong because they act on different bases; the product is what matters. The revenue would be unchanged only if volume rose by \( \tfrac{1}{0.75} - 1 = 33.3\% \).

Answer: C

The commission is deducted from the marked price, so the Rs. 9595 is 95% of it.

\[ \text{MP} \times (1 - 0.05) = 9595 \]

\[ \text{MP} = \frac{9595}{0.95} = \text{Rs. } 10100 \]

Checking: 5% of 10100 is 505, and \( 10100 - 505 = 9595 \).

Adding 5% to Rs. 9595 gives Rs. 10,074.75, which is not the answer - a percentage taken off a larger base cannot be undone by adding the same percentage to the smaller one.

Answer: C

Compare the two schemes by the fraction of the price that survives them.

20% then 20%:

\[ 800 \times 0.80 \times 0.80 = 800 \times 0.64 = \text{Rs. } 512 \]

30% then 10%:

\[ 800 \times 0.70 \times 0.90 = 800 \times 0.63 = \text{Rs. } 504 \]

\[ \text{extra saving} = 512 - 504 = \text{Rs. } 8 \]

Both schemes total 40% on paper, yet the more lopsided split wins. In general \( (1-a)(1-b) = 1 - a - b + ab \), so for a fixed sum \( a+b \) the retained fraction shrinks as the product \( ab \) shrinks - and \( 0.30 \times 0.10 = 0.03 \) is smaller than \( 0.20 \times 0.20 = 0.04 \).

Answer: C

Apply the known discount first, then see what fraction of the remainder she actually paid.

\[ 560 \times (1 - 0.20) = \text{Rs. } 448 \]

\[ \frac{336}{448} = 0.75 \quad\Longrightarrow\quad \text{second discount} = 1 - 0.75 = 25\% \]

Checking: \( 448 \times 0.75 = 336 \).

Taking \( \dfrac{560 - 336}{560} = 40\% \) gives the combined discount, not the second one - and indeed \( 1 - 0.80 \times 0.75 = 0.40 \).

Answer: C

Work through the first discount, then compare what is left with the selling price.

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

\[ \frac{612}{720} = 0.85 \quad\Longrightarrow\quad \text{second discount} = 15\% \]

Checking: \( 720 \times 0.85 = 612 \).

The combined discount here is \( 1 - 0.90 \times 0.85 = 23.5\% \), which is \( \dfrac{800-612}{800} \) - but the question asks only for the second step.

Answer: D

Successive discounts multiply the retained fractions.

\[ (1 - 0.20)(1 - 0.15) = 0.80 \times 0.85 = 0.68 \]

\[ \text{single equivalent discount} = 1 - 0.68 = 0.32 = 32\% \]

The general formula is

\[ a + b - \frac{ab}{100} = 20 + 15 - \frac{300}{100} = 32\% \]

Simply adding the two gives 35%, which is why that value is offered; 68% is the fraction retained, not the discount.