Question

A shopkeeper loses 7% by selling a cricket ball for Rs.31 how much he should sell a ball is a gain of 5%

Answer 1

Answer:

When the shopkeeper sells the cricket ball for rupees 31, he loses 7%.

Now, we know that:-

$\mapsto\tt{\underline{CP=SP+Loss\:\%\:of\:SP}}$

So, $\mapsto\tt{CP=31+\bigg(\dfrac{7}{100}\times 31}\bigg)$

$\mapsto\tt{CP=31+\bigg(\dfrac{7}{100}\times 31}\bigg)$

$\mapsto\tt{CP=31+ 2.17}$

$\mapsto\tt{CP=33.17\:Rupees}$

$\rule{200}2$

Now,what will be the price of the ball if the gain percent is 5%.

CP = Rs. 33.17

SP = CP + 5% of 33.17

$\mapsto\tt{SP=33.17+\bigg(\dfrac{5}{100}\times 33.17}\bigg)$

$\mapsto\tt{CP=33.17+ 1.6585}$

$\huge\mapsto\green{\tt{CP=34.8285\approx 35\: Rupees}}$

$\rule{200}4$

Answer 2

Answer:

⇢ Selling price should be = Rs.35

Step-by-step explanation:

Given:-

• Selling price = Rs.31
• Loss% = 7%

To find:-

• Selling price = ? if gain% = 5%

Solution:-

Let the cost price be Rs.M

We know,

$\star\: {\boxed{\sf\blue{Cost\: price = Selling \: price + Loss }}}$

$\dashrightarrow\sf M = 31 + M \times 7\% \\\\\dashrightarrow\sf M = 31 + \dfrac{7M}{100}\\\\\dashrightarrow\sf M - \dfrac{7M}{100} = 31 \\\\\dashrightarrow\sf \dfrac{100M - 7M}{100}= 31 \\\\\dashrightarrow\sf 93M = 3100 \\\\\dashrightarrow\sf M = \dfrac{3100}{93}\\\\\dashrightarrow\large{\underline{\boxed{\sf\green{Cost \: price(M) = Rs.33.33 }}}}$

Now,

$\star\:{\boxed{\sf\red{Selling \: price = Cost \: price + Gain}}}$

$\dashrightarrow\sf Selling \:price = 33.33 + 33.33 \times 5\% \\\\\dashrightarrow\sf Selling \:price = 33.33 + 1.6665 \\\\\dashrightarrow\large{\underline{\boxed{\sf\blue{Selling \: price = Rs.35}}}}$

$\therefore{\underline{\rm{Selling \: price \: should \: be = Rs.35}}}$