Question

by selling a TV set a retailer suffered a loss of 5% had he sold it for rupees 2880 more he would have received a profit of 10% what was the CP of the TV set​

Answer 1

$\tt\large\underline\purple{Let:-}$

$\tt{\implies Cost\: price\:_{(TV\:set)}=x}$

$\tt\large\underline\purple{To\: Find:-}$

$\tt{\implies Cost\: price\:_{(TV\:set)}=?}$

$\tt\large\underline\purple{Solution:-}$

To calculate the cost price of TV set at first we have to set up equation by helping clue in question.

$\sf\small\underline\red{Calculation\:for\:1st\: equation:-}$

• $\tt\underline{CP = x.\:\:\:L=5\%\:\:SP=?}$

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

$\tt{\implies SP=\bigg[\dfrac{100 - 5}{100}\times\:x\bigg]}$

$\tt{\implies SP=\bigg[\dfrac{95x}{100}\bigg]}$

• Now adding 2880 here :-]

$\tt{\implies SP=\bigg[\dfrac{95x}{100}+2880\bigg]------(i)}$

$\sf\small\underline\red{Calculation\:for\:1st\: equation:-}$

• $\tt\underline{CP = x.\:\:\: P=10\%\:\:SP=?}$

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

$\tt{\implies SP=\bigg[\dfrac{100 + 10}{100}\times\:x\bigg]}$

$\tt{\implies SP=\bigg[\dfrac{110x}{100}\bigg]------(ii)}$

• $\tt{Putting\:SP\:_{(eq.1)}=SP\:_{(eq.2)}}$

$\tt{\implies \bigg[\dfrac{110x}{100}\bigg]=\bigg[\dfrac{95x}{100}+2880\bigg]}$

$\tt{\implies \bigg[\dfrac{110x}{100}\bigg]-\bigg[\dfrac{95x}{100}\bigg]=2880}$

$\tt{\implies \bigg[\dfrac{110x-95x}{100}\bigg]=2880}$

$\tt{\implies \bigg[\dfrac{15x}{100}\bigg]=2880}$

$\tt{\implies 15x = 2880\times\:100}$

$\tt{\implies x = 192\times\:100}$

$\tt{\implies x = 19200}$

$\bf\small\underline{Hence, \:Cost\: price\:_{(TV\:set)}=Rs.19200}$

Answer 2

Let the CP of the TV set be Rs x

When loss = 5%, i.e r = 5

$\sf{\red{\large{SP = (1 - \frac{r}{100})CP}}}$

$\sf{SP = (1 - \frac{5}{100})x =Rs \:0.95x}$

When profit = 10%, i.e r = 10

SP = 0.95x + 2880

But,

$\sf{\red{\large{SP = (1 + \frac{r}{100})CP}}}$

So,

$\sf{0.95x + 2880 = (1 + \frac{10}{100})x}$

$\sf{0.95x + 2880 = 1.1x}$

$\sf{1.1x - 0.95x = 2880}$

$\sf{0.15x = 2880}$

$\sf{ = 19200}$

Therefore, the CP of TV set is Rs 19200