True Discount Questions and Answers

Answer: D

Take the cost price as 100 and let the labelled price be \( M \). After a 10% discount the seller must still clear a 20% profit.

\[ M \times (1 - 0.10) = 100 \times 1.20 \]

\[ 0.9M = 120 \quad\Longrightarrow\quad M = \frac{120}{0.9} = 133.33 \]

\[ \text{increase over cost} = 133.33 - 100 = 33\tfrac{1}{3}\% \]

Adding 20% and 10% to get 30% is the trap: the profit is measured on the cost price while the discount comes off the labelled price, so the two act on different bases.

Answer: B

Four quantities are related throughout this topic. Writing \( k = \dfrac{RT}{100} \):

\[ \text{BD} = A\,k, \qquad \text{TD} = \frac{A\,k}{1+k} = \text{PW}\,k, \qquad \text{BG} = \text{BD} - \text{TD} = \text{TD}\,k \]

The banker's discount is interest on the face value; the true discount is interest on the present worth; the banker's gain is the interest on the true discount.

\[ \text{PW} = 540 - 90 = \text{Rs. } 450 \quad\Longrightarrow\quad k = \frac{\text{TD}}{\text{PW}} = \frac{90}{450} = 0.2 \]

\[ \text{BD} = A\,k = 540 \times 0.2 = \text{Rs. } 108 \]

The banker's discount always exceeds the true discount, here by \( 108 - 90 = \text{Rs. } 18 \), because it charges interest on the larger face value.

Answer: C

Convert the order to dozens first, since both the price and the discount threshold are quoted per dozen.

\[ \frac{3000}{12} = 250 \text{ dozen} \]

That exceeds 12 dozen, so the 15% discount applies to the whole order.

\[ \text{list price} = 250 \times 100 = \text{Rs. } 25000 \]

\[ \text{payable} = 25000 \times 0.85 = \text{Rs. } 21250 \]

The discount applies to the entire order once the threshold is crossed, not only to the dozens above 12 - charging full price for the first 12 dozen would give Rs. 21,430.

Answer: A

Four quantities are related throughout this topic. Writing \( k = \dfrac{RT}{100} \):

\[ \text{BD} = A\,k, \qquad \text{TD} = \frac{A\,k}{1+k} = \text{PW}\,k, \qquad \text{BG} = \text{BD} - \text{TD} = \text{TD}\,k \]

The banker's discount is interest on the face value; the true discount is interest on the present worth; the banker's gain is the interest on the true discount.

With \( k = \dfrac{5 \times 2}{100} = 0.1 \):

\[ \text{TD} = \frac{\text{BG}}{k} = \frac{80}{0.1} = \text{Rs. } 800 \]

\[ \text{PW} = \frac{\text{TD}}{k} = \frac{800}{0.1} = \text{Rs. } 8000 \]

Rs. 800 is only the true discount, one step short of the answer. As a check, the face value is \( 8000 + 800 = 8800 \) and the banker's discount is \( 8800 \times 0.1 = 880 \), exactly Rs. 80 above the true discount.

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: D

True discount is simple interest on the present worth, so the present worth follows directly.

With \( T = \dfrac{9}{12} = 0.75 \) year at 12%:

\[ k = \frac{12 \times 0.75}{100} = 0.09 \]

\[ \text{PW} = \frac{\text{TD}}{k} = \frac{540}{0.09} = \text{Rs. } 6000 \]

The bill itself is \( 6000 + 540 = \text{Rs. } 6540 \). Dividing the discount by \( k \) always lands on the present worth; the face value needs the discount added back.

Answer: B

S.I on Rs.750= T.D on Rs. 960 

This means P.W of Rs. 960 due 2 years hence is Rs.750 

Therefore , T.D= Rs. (960 - 750) = Rs. 210 

Thus, S.I on Rs. 750 for 2 years is Rs. 210 

Rate =[ (100 x 210) / (750 x 2) ] % = 14%

Answer: C

Four quantities are related throughout this topic. Writing \( k = \dfrac{RT}{100} \):

\[ \text{BD} = A\,k, \qquad \text{TD} = \frac{A\,k}{1+k} = \text{PW}\,k, \qquad \text{BG} = \text{BD} - \text{TD} = \text{TD}\,k \]

The banker's discount is interest on the face value; the true discount is interest on the present worth; the banker's gain is the interest on the true discount.

With \( k = \dfrac{12 \times 3}{100} = 0.36 \):

\[ \text{BG} = \text{TD} \times k \quad\Longrightarrow\quad \text{TD} = \frac{270}{0.36} = \text{Rs. } 750 \]

\[ \text{BD} = \text{TD} + \text{BG} = 750 + 270 = \text{Rs. } 1020 \]

Rs. 750 is the true discount, an intermediate step; the banker's discount is always the larger of the two, exceeding it by exactly the banker's gain.

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: D

Successive discounts multiply; they do not add to 30%.

\[ \text{SP} = 500 \times (1 - 0.20) \times (1 - 0.10) \]

\[ = 500 \times 0.80 \times 0.90 = 500 \times 0.72 = \text{Rs. } 360 \]

The equivalent single discount is 28%, not 30%: the second 10% is charged on Rs. 400 rather than on Rs. 500, so it saves Rs. 40 instead of Rs. 50. Adding the discounts would give Rs. 350, which is the listed trap.