Question

6) Successive discounts of 20% and 20%
are equivalent to a single discount of
(a) 40%
(b) 45%
(c) 50%
(d) 36%​

Answer 1

Required Answer:-

Here we have two successive discounts. We can directly use the formula for determining the final discount. The formula says:

• $\underline{\boxed{ \bf{Total \: Discount = x + y - \frac{ xy}{100} \%}}}$

Where x and y are successive discounts. Plugging them in this formula gives:

➙ Total discount = 20 + 20 - 20*20/100 %

➙ Total discount = 40 - 4 %

➙ Total discount = 36% (D)

━━━━━━━━━━━━━━━━━━━━

Now let's take an example to understand the above formula. We have to take amy amount. For convenience, I am choosing Rs. 100 for an item.

First discount:

= Rs. 100 - 20% discount

= Rs. 100 - 20/100 × Rs. 100

= Rs. 100 - Rs. 20

= Rs. 80

Second discount:

= Rs. 80 - 20% discount

= Rs. 80 - 20/100 × Rs. 80

= Rs. 80 - Rs. 16

= Rs. 64

Hence, Final amount will be Rs. 64. Amount in total discount = Rs. 100 - Rs. 64 = Rs. 36 which 36% as a total discount for the given amount.

Answer 2

Given :-

• Successive Discount of 20% and 20% are equivalent to a single Discount

To Find :-

Single Discount

Theory :-

Firstly we will assume the two discount as x and y. Then, the x and y will be put in an equation which is

$\sf \: Discount = x + y - \dfrac{xy}{100}\%$

Now,

We will put the Discount percentage

Solution :-

$\sf \implies \: Discount = 20 + 20 - \dfrac{20 \times 20}{100}$

$\sf \implies \: Discount = 40 - \dfrac{20 \times 20}{100}$

$\sf \implies \: Discount = 40 - \cancel\dfrac{400}{100}$

$\sf \implies \: Discount = 40 - 4$

$\frak \pink{Discount = 36\%}$

Hence :-

Option (D) is correct