Question

If an article is sold on 4x% discount then it sold at 20% loss and if only x% discount is given then it sold at 25% profit. Find the value of "x" (approximately)

Answer 1

Answer-

The value of x is 11.

Solution-

Let us assume the cost price to be 100 and list price as y.

In first case the article is sold on 4x % discount on a list price of y, so selling price would be,

$=y-y\times \frac{4x}{100} =y(1-\frac{4x}{100})$

And as it is sold at 20% loss on a cost price of 100, so selling price would be,

$=100-100\times \frac{20}{100} =100-20=80$

As selling price is same, so

$\Rightarrow y(1-\frac{4x}{100})=80$   --------------------1

In second case the article is sold on x % discount on a list price of y, so selling price would be,

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

And as it is sold at 25% profit on a cost price of 100, so selling price would be,

$=100+100\times \frac{25}{100} =100+25=125$

As selling price is same, so

$\Rightarrow y(1-\frac{x}{100})=125$   --------------------2

Dividing eq 1 and 2,

$\Rightarrow \frac{y(1-\frac{4x}{100})}{y(1-\frac{x}{100})}=\frac{80}{125}$

$\Rightarrow \frac{(1-\frac{4x}{100})}{(1-\frac{x}{100})}=\frac{80}{125}$

$\Rightarrow \frac{(\frac{100-4x}{100})}{(\frac{100-x}{100})}=\frac{16}{25}$

$\Rightarrow \frac{100-4x}{100-x}=\frac{16}{25}$

$\Rightarrow 2500-100x=1600-16x$

$\Rightarrow 84x=900$

$\Rightarrow x=\frac{900}{84}$

$\Rightarrow x=10.7$

$\Rightarrow x\approx 11$

Therefore, the value of x is 11.