Successive discounts of p% and q% on an invoice is the same as a single discount of Option 1: [p+q-pq/100]% Option 2: [p-q+pq/100]% Option 3: 100-[p+q+pq/100]% Option 4: [p+q+pq/100]%

Answer: [p+q-pq/100]%. Solution: Take the original price as 100, since we want the answer as a percentage. After the first discount of p%, the price left is 100-p The second discount of q% applies to this reduced price: (100-p)-q/100(100-p) =(100-p)(1-q/100) =100-p-q+pq/100 Total discount=starting price-final price =100-(100-p-q+pq/100) =p+q-pq/100 Since we started from 100, this number is already the percentage: [p+q-pq/100]% The minus sign makes sense, because the second discount is taken on a smaller price, so you save a little less than p+q.

Arithmetic

Percentages

Easy

Successive discounts of $p\%$ and $q\%$ on an invoice is the same as a single discount of

$\left[p+q-\dfrac{pq}{100}\right]\%$

$\left[p-q+\dfrac{pq}{100}\right]\%$

$100-\left[p+q+\dfrac{pq}{100}\right]\%$

$\left[p+q+\dfrac{pq}{100}\right]\%$

✅ Correct Option: 1

Take the original price as 100, since we want the answer as a percentage.

After the first discount of $p\%$ , the price left is

$100-p$

The second discount of $q\%$ applies to this reduced price:

$(100-p)-\dfrac{q}{100}(100-p)$

$=(100-p)\left(1-\dfrac{q}{100}\right)$

$=100-p-q+\dfrac{pq}{100}$

$\text{Total discount}=\text{starting price}-\text{final price}$

$=100-\left(100-p-q+\dfrac{pq}{100}\right)$

$=p+q-\dfrac{pq}{100}$

Since we started from 100, this number is already the percentage:

$\left[p+q-\dfrac{pq}{100}\right]\%$

The minus sign makes sense, because the second discount is taken on a smaller price, so you save a little less than $p+q$ .

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A candidate scoring $x \%$ marks in an examination fails by ' $a$ ' marks while another candidate who scores $y \%$ marks, gets ' $b$ ' marks more than the minimum required pass marks. What is the maximum marks for the examination ?

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Match the LIST-I with LIST-II

	LIST-I (Expression)		LIST-II (Value)
A.	$(550\%\text{ of }250) \div 275$	I.	129.58
B.	$38\%\text{ of }341$	II.	231.6
C.	$15\%\text{ of }578+22.5\%\text{ of }644$	III.	156.8
D.	$140\%\text{ of }56+56\%\text{ of }140$	IV.	5

Choose the correct answer from the options given below:

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If the difference between 62% and 80% of a number is 198, then the difference between 92% and 56% of the same number will be :-

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The value of a flat worth ₹500,000 is depreciating at the rate of 10% per annum. In how many years will the value be reduced to ₹364,500?

JIPMAT 2021

A train starts full of passengers. At the first station, it drops one third of passengers and takes 280 more. At the second station, it drops one half of the new total and takes 12 more. On arriving at the third station, it is found to have 248 passengers. The number of passengers in the beginning was

Successive discounts of p%p\%p% and q%q\%q% on an invoice is the same as a single discount of

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