Tag: successive discounts

Questions Related to successive discounts

$50$% discount + $20$% discount = ____%discount

maths money math different discounts successive discounts problems on discounts

  1. $60$

  2. $65$

  3. $40$

  4. $70$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  Let $x$ be the first discount $50\%$ and $y$ be the second discount $20\%$.


$\Rightarrow$   Total Discount = $(x+y-\dfrac{xy}{100})\%$

$\Rightarrow$   Total discount = $(50+20-\dfrac{50\times 20}{100})\%$

$\Rightarrow$   Total discount = $(70-\dfrac{1000}{100})\%=60\%$

$\therefore$    $50\%$ discount + $20\%$ discount = $60\%$ discount.

Find a single discount equivalent to following successive discounts of $20\%$, $10\%$ and $50\%$ in percent.

maths money math different discounts successive discounts problems on discounts

  1. $54\%$

  2. $64\%$

  3. $74\%$

  4. $84\%$

Show answer
Correct Option: B
Explanation:

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

$\Rightarrow$   $(20+10-\dfrac{20\times 10}{100})\%=28\%$

$\Rightarrow$  Single discount equivalent for successive discounts of $28\%$ and $50\%$.
$\Rightarrow$   $(28+50-\dfrac{28\times 50}{100})\%=64\%$

$50$% discount + $50$% discount = ____%discount

maths money math different discounts successive discounts problems on discounts

  1. $75$

  2. $50$

  3. $100$

  4. $60$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  Let $x$ be the first discount $50\%$ and $y$ be the second discount $50\%$.


$\Rightarrow$   Total Discount = $(x+y-\dfrac{xy}{100})\%$

$\Rightarrow$   Total discount = $(50+50-\dfrac{50\times 50}{100})\%$

$\Rightarrow$   Total discount = $(100-\dfrac{2500}{100})\%=75\%$

$\therefore$    $50\%$ discount + $50\%$ discount = $75\%$ discount.

After getting three equal successive discounts percentages over a marked price of Rs. $1000$ a customer has to pay $512$ for an article. What is the rate of each of the successive discounts ?

maths money math different discounts successive discounts problems on discounts

  1. $5$%

  2. $10$%

  3. $15$%

  4. $20$%

Show answer
Correct Option: D
Explanation:

Let the discount price be$x$.

After the first discount, price$=(1-x)1000$
After the second discount, price$=(1-x)(1-x)1000=(1-x)^21000$
After the third discount, price$=(1-x)(1-x)(1-x)1000=(1-x)^3 1000$
According to the question 
$(1-x)^3 1000=512\(1-x)^3=512/1000\(1-x)=8/10\x=1/5$
Required percentage is $(1/5)\times 100=20\%$.

$50$% discount + $40$% discount = ____%discount

maths money math different discounts successive discounts problems on discounts

  1. $60$

  2. $70$

  3. $80$

  4. $90$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Let $x$ be the first discount $50\%$ and $y$ be the second discount $40\%$.


$\Rightarrow$   Total Discount = $(x+y-\dfrac{xy}{100})\%$

$\Rightarrow$   Total discount = $(50+40-\dfrac{50\times 40}{100})\%$

$\Rightarrow$   Total discount = $(90-\dfrac{2000}{100})\%=70\%$

$\therefore$    $50\%$ discount + $40\%$ discount = $70\%$ discount.

Find a single discount equivalent to following successive discounts of $50\%$, $10\%$ and $20\%$ in percent.

maths money math different discounts successive discounts problems on discounts

  1. $54\%$

  2. $64\%$

  3. $74\%$

  4. $84\%$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Single discount equivalent for successive discounts of $50\%$ and $10\%$.

$\Rightarrow$   $(50+10-\dfrac{50\times 10}{100})\%=55\%$

$\Rightarrow$  Single discount equivalent for successive discounts of $55\%$ and $20\%$.
$\Rightarrow$   $(55+20-\dfrac{55\times 20}{100})\%=64\%$

If the difference between a discount of 25% and two successive discounts of 15% and 10% is ' 63, then the marked price of the article is

maths money math different discounts successive discounts problems on discounts

  1. Rs. $4200$

  2. Rs. $6400$

  3. Rs. $2100$

  4. Rs. $3200$

Show answer
Correct Option: A
Explanation:

Let the marked price be $M$


After $25\%$  discount price will be $0.75M$

And the price after 2 successive discounts of $15\%$ and $10\%=0.85M\times 0.9=0.765M$.

Difference $\Rightarrow 0.765 M-0.75M=0.015M=63\implies M=4200$

The difference between a discount of $60\%$ on Rs. $500$ and two successive discounts of $36\%$ and $4\%$ on the same amount is __________.

maths money math different discounts successive discounts problems on discounts

  1. $0$

  2. Rs. $2$

  3. Rs. $1.93$

  4. Rs. $7.20$

Show answer
Correct Option: D
Explanation:

Discount of $60\%$ on $500 = 0.6\times 500=300$

Two successive discounts of $36\% $ and $4\%$.
$= (1-0.36)\times 500(1-0.04) = 307.2$
Difference in both the discounts is $307.2 - 300= 7.2$.

On a Rs.$10,000$ order a merchant has a choice among three successive discounts of $20\%, 20\% and 10\%$ and three successive discounts of $40\%, 5\% and 5\%$. By choosing the best offer, he can save:

maths money math different discounts successive discounts problems on discounts

  1. nothing at all

  2. Rs.$400$

  3. Rs.$330$

  4. Rs.$345$

  5. Rs.$360$

Show answer
Correct Option: D
Explanation:

Since a single discount D, equal to three successive discounts $D _1, D _2 and D _3$ is $D = D _1 + D _2 + D _2 - D _1D _2 - D _2D _3 - D _3D _1 + D _1D _2D _3$, then the choices are
$0.20 + 0.20 + 0.10 - 0.04 - 0.02 - 0.02 + 0.004 = 0.424$ and $0.40 + 0.05 + 0.05 - 0.02 - 0.02 - 0.0025 + 0.001 = 0.4585.$
The saving is $0.0345.10,000 = 345 rupees$

Applied to a bill for Rs. $10,000$ the difference between a discount of $40\%$ and two successive discounts of $36\%$ and $4\%$, expressed in rupees, is

maths money math different discounts successive discounts problems on discounts

  1. $0$

  2. $1440$

  3. $2560$

  4. $4000$

  5. $416$

Show answer
Correct Option: B
Explanation:

$40$% of $Rs. 10,000$ is $Rs. 4,000; 36$% of $Rs. 10,000$ is $Rs. 3,600; 4$% of $(Rs. 10,000 - Rs. 3,600)$ is $Rs. 256. Rs. 3,600 + Rs. 256 = Rs. 3,856$;
$\therefore$ the difference is $Rs. 4,000 - Rs. 3,856 = Rs. 144$; or two successive discounts of $36$% and $4$% are equivalent to one discount of $38.56$%.

∴ Percentage difference = $40$ – $38.56$ = $1.44%$
Difference between discount = $1.44%$ of $100000$
=$\dfrac{1.44\times10000}{100}=1440Rs$