Question

16. A dealer sells a toy at a loss of 4%. If he had sold it for 180 more, he would have made
profit of 16%. Find the cost price of the toy.
​

Answer 1

$\sf\small\underline\green{Let:-}$

$\tt{\implies Cost\: price\:of\:toy=x}$

$\sf\small\underline\green{Given:-}$

$\tt{\implies Loss\:on\:selling=4\%}$

$\sf\small\underline\green{To\:Find:-}$

$\tt{\implies Cost\: price\:of\:toy=?}$

$\sf\small\underline\green{Solution:-}$

$\sf{\implies calculation\:for\:case-(i)}$

$\bf\small\underline{SP=?\:\:CP=x\:\:L=4\%:-}$

$\tt{\implies SP=\bigg[\dfrac{100-L\%}{100}\bigg]\times\:CP}$

$\tt{\implies SP=\bigg[\dfrac{100-4}{100}\bigg]\times\:x+180}$

$\tt{\implies SP=\bigg[\dfrac{96}{100}\bigg]\times\:x+180}$

$\tt{\implies SP=\bigg[\dfrac{96x}{100}\bigg]+180----(i)}$

$\sf{\implies calculation\:for\:case-(ii)}$

$\bf\small\underline{SP=?\:\:CP=x\:\:P=16\%:-}$

$\tt{\implies SP=\bigg[\dfrac{100+P\%}{100}\bigg]\times\:CP}$

$\tt{\implies SP=\bigg[\dfrac{100+16}{100}\bigg]\times\:x}$

$\tt{\implies SP=\bigg[\dfrac{116}{100}\bigg]\times\:x}$

$\tt{\implies SP=\bigg[\dfrac{116x}{100}\bigg]---(ii)}$

$\bf{\implies Case-(ii)=Case-(i)}$

$\tt{\implies \dfrac{116x}{100}=\dfrac{96x}{100}+180}$

$\tt{\implies \dfrac{116x}{100}-\dfrac{96x}{100}=180}$

$\tt{\implies \dfrac{116x-96x}{100}=180}$

$\tt{\implies \dfrac{20x}{100}=180}$

$\tt{\implies 20x=18000}$

$\tt{\implies x=900}$

$\sf\large{Hence,}$

$\bf{\implies The\:cost\: price\:of\:toy=900}$

Answer 2

Given :-

A dealer sells a toy at a loss of 4%. If he had sold it for 180 more, he would have made  profit of 16%.

To Find :-

CP of toy

Solution :-

Let the CP of toy be x

We know that

$\sf SP = \dfrac{(100-Loss\%)}{100}CP$

$\sf SP = \dfrac{100 - 4}{100}(x+180)$

$\sf SP = \dfrac{96}{100}x+180$

$\sf SP = \dfrac{96x}{100} + 180$

Now

$\sf SP = \dfrac{(100-profit\%)}{100}CP$

$\sf SP = \dfrac{100 + 16}{100} x$

$\sf SP = \dfrac{116}{100}x$

Now

116x/100 -  96x/100 = 180

20x/100 = 180

x/5 = 180

x = 180 $\times$5

x = 900