Question

Two consecutive discounts x% and y% is equivalent to the discount

Answer 1

Answer:

(x+y-xy100)%

Step-by-step explanation:

Hope it helps!!

Answer 2

Answer:

The equivalent discount will be $(x + y - \frac{xy}{100} )\%$.

Step-by-step explanation:

Given,

The problem is to find an equivalent discount to two consecutive discounts of x% and y%.

So, let us take the Price to be = A

Now we will find the cost after x% discount -

$=A - A\times x\%\\\\= A - A\times \frac{x}{100} \\\\=A(1-\frac{x}{100} )$

Now again applying a y% discount to this price -

$= A(1-\frac{x}{100} ) - A(1-\frac{x}{100} )y\%\\\\= A(1-\frac{x}{100} )-A(1-\frac{x}{100} )\frac{y}{100} \\\\=A(1-\frac{x}{100} )(1-\frac{y}{100} )\\\\= A(1-\frac{x}{100} -\frac{y}{100} +\frac{xy}{10000} )$

We got the price after consecutive discounts of x% and y%.

Now let the discount of z% is equal to this price. So if we do the same steps we will get a value of z.

$A - Az\% = A(1-\frac{x}{100} -\frac{y}{100} +\frac{xy}{10000} )\\\\A - A\times \frac{z}{100} = A(1-\frac{x}{100} -\frac{y}{100} +\frac{xy}{10000} )\\\\1-\frac{z}{100} = 1-\frac{x}{100} -\frac{y}{100} +\frac{xy}{10000} \\\\z = x + y - \frac{xy}{100}$

So the equivalent discount will be $(x + y - \frac{xy}{100} )\%$.

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