Tag: successive discounts

Questions Related to successive discounts

Find the single discount equivalent to two successive discounts of $20\%$ and $45\%$.

maths money math different discounts successive discounts problems on discounts

  1. $50\%$

  2. $45\%$

  3. $10\%$

  4. $60.5\%$

Show answer
Correct Option: D
Explanation:

Total discount $=$ $20+45-\dfrac{450}{100}=60.5\%$
The single discount equivalent to two discount $ = 60.50\%$ 

The marked price of a ceiling fan is Rs. $1250$ and the shopkeeper allows a discount of $6\%$ on it. Find the selling price of the fan.

maths money math different discounts successive discounts problems on discounts

  1. $1175$

  2. $2260$

  3. $1150$

  4. $1460$

Show answer
Correct Option: A
Explanation:

Given, marked price $=$ Rs. $1250$ and discount $=6\%$

Discount $=6\%$ of marked price
$=6\%$ of $1250$
$=\dfrac {6}{100}\times 1250$
$=75$
Selling price $=$ Marked price $-$ Discount
$=1250-75$
$=1175$
Hence, the selling price of the fan is Rs. $1175$.

The original price $P$ of a certain item is first discounted by $20$ percent and then $5$ percent of the discount price is added for sales tax. If the final price, including the sales tax is $\$71.40$, calculate the original price $P$.

maths money math different discounts successive discounts problems on discounts

  1. $\$59.50$

  2. $\$81.40$

  3. $\$84.00$

  4. $\$85.00$

  5. $\$86.40$

Show answer
Correct Option: D
Explanation:

Given, $P$ is the original price of item and get $20\%$ discount. 

Then discounted price $=$$\dfrac{80}{100}P=\dfrac{4}{5}P$
Then sale  tax $5\%$ on discounted price $=$ $\dfrac{5}{100}\times \dfrac{4}{5}P=\dfrac{1}{25}P$.
Then total cost $=$ $\dfrac{4}{5}P+\dfrac{1}{25}P$
But total cost is $71.40$ ....... (given) 
Therefore, $ \dfrac{4}{5}P+\dfrac{1}{25}P=71.40$
$\Rightarrow 20P+P=1785$
$\Rightarrow 21P=1785$
$\Rightarrow P=85$

If there is a discount of $30\%$ on a speaker and Mira gets another discount of $20\%$ through her coupon, calculate the price paid by her to buy the speaker, if the original price is $\$100$.

maths money math different discounts successive discounts problems on discounts

  1. $ $86.00$

  2. $ $77.60$

  3. $ $56.00$

  4. $ $50.00$

  5. $ $44.00$

Show answer
Correct Option: C
Explanation:

There is a initial 30% discount on a $\$ 100$ speaker. This reduces its cost to $\$ 70$. 

Now there is another $20\%$ discount on it. 
Hence, its final price will be $(1-\dfrac{20}{100})\times 70$
$=(1-\dfrac{1}{5})\times 70$
$=\dfrac{4}{5}\times 70=$ 56$

A real estate agent puts a house on the market at a higher-than-expected selling price. If the house is not sold in two weeks, then he drops the price by $5\%$, again if it is still not sold in next two weeks, then he drops the price by another $5\%$. After that, he continues to drop the price by $3\%$ every two weeks until it reaches a cut-off amount decided by the home-owner, or the house sells, whichever comes first. If originally house is listed at $ $200,000$ and owner sets a cut-off amount of $ $166,000$, what is the final selling price given that the house sells after being on the market for $9$ weeks?

maths money math different discounts successive discounts problems on discounts

  1. $\$162,901.25$

  2. $\$164,737.48$

  3. $\$166,000.00$

  4. $\$169,832.45$

Show answer
Correct Option: D
Explanation:

Listed price of house $=200,000$ USD

Week $1$ & $2$ $\Longrightarrow$ Price remains same


Week $3$ & $4$ $\Longrightarrow$ $5\%$ reduction in $200,000$ USD

The new price is $200000 \times \dfrac {95}{100} = 190,000$ USD


Week $5$ & $6$ $\Longrightarrow$ $5\%$ reduction in $190,000$ USD
The new price is $190000 \times \dfrac {95}{100} = 180,500$ USD


Week $7$ & $8$ $\Longrightarrow$ $3\%$ reduction in $180,500$ USD
The new price is $180500 \times \dfrac {97}{100} = 175,085$ USD


Week $9$ $\Longrightarrow$ $3\%$ reduction in $175,085$ USD
The new price is $175,085 \times \dfrac {97}{100} = 169,832.45$ USD

Find the difference between a discount of $40\%$ and two successive discounts of $36\%$ and $4\%$ for Rs. $10,000$.

maths money math different discounts successive discounts problems on discounts

  1. Rs. $0$

  2. Rs. $144$

  3. Rs. $256$

  4. Rs. $400$

Show answer
Correct Option: B
Explanation:
Single equivalent discount of two successive discounts of $36\%$ and $4\%$ is,
$\Rightarrow$   $36+4-\dfrac{36\times 4}{100}$
$\Rightarrow$    $40 - 1.44 = 38.56$
$\Rightarrow$Percentage difference = $40 - 38.56 = 1.44$
$\therefore$  Required Difference = $10,000\times \dfrac{1.44}{100} =Rs.144$

The difference between the discounts of $40\%$ on Rs. $5000$ and two successive discounts of $36\%$ and $4\%$ on the same price is :

maths money math different discounts successive discounts problems on discounts

  1. Rs. $62$

  2. Rs. $72$

  3. Rs. $19.3$

  4. Rs. $20$

Show answer
Correct Option: B
Explanation:

Single equivalent discount of two successive discounts of $36\%$ and $4\%\,\,:$

$\Rightarrow$ $36+4-\dfrac{36\times 4}{100}=40-1.44=38.56\%$
Percentage difference $=$ $(40-38.56)\%=1.44\%$
Thus required difference $=$ $5000\times \dfrac{1.44}{100}=$ Rs. $72$

Find a single discount equivalent to the successive discounts of $10\%, 20\%$ and $20\%$ (in percent).

maths money math different discounts successive discounts problems on discounts

  1. $42.1\%$

  2. $42.4\%$

  3. $42.8\%$

  4. $45\%$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Single equivalent discount for successive discount of $10\%$ and $20\%$.

$\Rightarrow$  $[10+20-\dfrac{20\times 10}{100}]\%=28\%$
$\Rightarrow$   Single equivalent discount for $28\%$  and $20\%$

$\Rightarrow$   $[28+20-\dfrac{28\times 20}{100}]\%=42.4\%$

After getting three equal successive discounts percentages over a marked price of Rs. $1000$ a customer has to pay $729$ for an article. What is the rate of each of the successive discounts ?

maths money math different discounts successive discounts problems on discounts

  1. $10\%$

  2. $20\%$

  3. $30\%$

  4. $40\%$

Show answer
Correct Option: A
Explanation:

Let $x$ is the factor by which successive discount was given.

Thus $1000\times x\times x\times x=729$
$\Rightarrow$ $x^3=\dfrac{729}{1000}$
$\Rightarrow$ $x=\dfrac{9}{10}$
$\Rightarrow$ $x=0.9\approx 10\%$

Pepsi and Coke, there are two companies , selling the packs of cold-drinks. For the same selling price Pepsi gives two successive discounts of $10$ % and $25$ %. While coke sells it by giving two successive discounts of $15$ % and $20$ %. what is the ratio of their marked price?

maths money math different discounts successive discounts problems on discounts

  1. $143 : 144$

  2. $43 : 44$

  3. $135 : 134$

  4. $136 : 135$

Show answer
Correct Option: D
Explanation:

$SP=MP-$discount$\times MP$

After first discount,
$(SP)'=(1-discount _1)\times MP$

After second discount,
$SP=(1-discount _1)(1-discount _2)\times MP$

For pepsi
$(SP) _1=(1-0.1)(1-0.25)\times (MP) _1$

For coke
$(SP) _2=(1-0.15)(1-0.2)\times (MP) _2$

We know that $(SP) _1=(SP) _2$
$\cfrac{(MP) _1}{(MP) _2}=\cfrac{0.85\times0.8}{0.9\times 0.75}=136/135=136:135$