True Discount Questions and Answers

Q: George gets a discount of 30% and then 20% on his food bill of Rs. 1250. What is the total discount he got?

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 \( 0.30 \times 0.20 = 6\% \).

Q: Blackberry announced a discount of 25% on their trousers. Vivek went to shop. He wanted to save Rs. 400 in discount. How many trousers should he buy to do so, if each trouser costs Rs. 320?

Work out what one trouser saves, then divide.\[ \text{saving per trouser} = 0.25 \times 320 = \text{Rs. } 80 \]\[ n = \frac{400}{80} = 5 \]So he must buy 5 trousers. Dividing the Rs. 400 target by the full Rs. 320 price instead gives 1.25 and tempts a rounding to 4 - but the saving, not the price, is what accumulates toward the target.

Q: If Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is

Recover the rate–time product from the original bill.\[ \text{PW} = 110 - 10 = 100 \quad\Longrightarrow\quad 100k = 10 \quad\Longrightarrow\quad k = 0.1 \]Doubling the time doubles \( k \) to 0.2, so\[ \text{PW}' = \frac{110}{1.2} = 91.67 \quad\Longrightarrow\quad \text{TD}' = 110 - 91.67 = \text{Rs. } 18.33 \]The discount grows, but by less than double: the present worth it is charged on falls at the same time, so the two effects partly cancel.

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101.

George gets a discount of 30% and then 20% on his food bill of Rs. 1250. What is the total discount he got?

A.44%
B.55%
C.52%
D.25%

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 \( 0.30 \times 0.20 = 6\% \).

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102.

Which of the following will yield maximum discount on Rs. 6896?

1) 2 successive discounts of 5% and 5%
2) Single discount of 10%
3) 2 successive discounts of 8% and 2%

A.3
B.2
C.1
D.All will yield same discount

Answer: B

Successive discounts multiply rather than add. For discounts \( a \) and \( b \) the price retained is \( (1-a)(1-b) \).

1) 5% then 5%:

\[ 0.95 \times 0.95 = 0.9025 \quad\Longrightarrow\quad \text{discount } 9.75\% \]

2) a single 10%:

\[ 0.90 \quad\Longrightarrow\quad \text{discount } 10\% \]

3) 8% then 2%:

\[ 0.92 \times 0.98 = 0.9016 \quad\Longrightarrow\quad \text{discount } 9.84\% \]

The single 10% is largest, so option 2 wins. Two discounts summing to 10% always fall short of a single 10%, because the second is applied to an already reduced price - the shortfall is the product \( ab \), here 0.25% and 0.16%.

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103.

The profit earned by selling an article for Rs. 900 is double the loss incurred when the same article is sold for Rs. 450. At what price should the article be sold to make a 25% profit?

A.715
B.469
C.400
D.750

Answer: D

Let the cost price be \( C \). Selling at Rs. 900 gives a profit of \( 900 - C \); selling at Rs. 450 gives a loss of \( C - 450 \).

\[ 900 - C = 2(C - 450) \]

\[ 900 - C = 2C - 900 \quad\Longrightarrow\quad 3C = 1800 \quad\Longrightarrow\quad C = \text{Rs. } 600 \]

Checking: the profit is Rs. 300 and the loss Rs. 150 - double, as required.

\[ \text{SP for 25\% profit} = 600 \times 1.25 = \text{Rs. } 750 \]

Averaging the two selling prices would give Rs. 675, which is the cost price only when profit and loss are equal - not the case here.

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104.

Blackberry announced a discount of 25% on their trousers. Vivek went to shop. He wanted to save Rs. 400 in discount. How many trousers should he buy to do so, if each trouser costs Rs. 320?

A.5
B.4
C.10
D.50

Answer: A

Work out what one trouser saves, then divide.

\[ \text{saving per trouser} = 0.25 \times 320 = \text{Rs. } 80 \]

\[ n = \frac{400}{80} = 5 \]

So he must buy 5 trousers. Dividing the Rs. 400 target by the full Rs. 320 price instead gives 1.25 and tempts a rounding to 4 - but the saving, not the price, is what accumulates toward the target.

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105.

When payment is made online, discount offered is 10%. Additional discount of 5% is given to SBI credit card holders. Pratik buys a phone of Rs. 15000 by paying online and pays through his SBI credit card. How much does he need to pay?

A.Rs. 15000
B.Rs. 12825
C.Rs. 13500
D.Rs. 12750

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.

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106.

If Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is

A.18.20
B.18.33
C.18
D.18.30

Answer: B

Recover the rate–time product from the original bill.

\[ \text{PW} = 110 - 10 = 100 \quad\Longrightarrow\quad 100k = 10 \quad\Longrightarrow\quad k = 0.1 \]

Doubling the time doubles \( k \) to 0.2, so

\[ \text{PW}' = \frac{110}{1.2} = 91.67 \quad\Longrightarrow\quad \text{TD}' = 110 - 91.67 = \text{Rs. } 18.33 \]

The discount grows, but by less than double: the present worth it is charged on falls at the same time, so the two effects partly cancel.

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