Question

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6. Jaya bought two sarees for 800 each. She sold one at a gain of 5% and other at a loss of 4%. Find
her gain or loss percent in the whole transaction.
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Answer 1

Step-by-step explanation:

lost on first saree =800÷5 = 160

Lost on second saree =800÷4= 200

Answer 2

Solution :

$\underline{\bf{Given\::}}$

Jaya bought two sarees for Rs.800 each . She sold one at a gain of 5% & other at a loss of 4% .

$\underline{\bf{Explanation\::}}$

$\underbrace{\bf{1^{st}\:case\::}}$

• Cost price of one saree, (C.P) = Rs.800
• She sells one saree at on gain = 5%
• Selling price = ?

A/q

Using formula of the selling price when show gain;

$\boxed{\bf{Selling\:price=\bigg(\frac{100+profit\%}{100} \bigg)\times C.P.}}$

$\longrightarrow\tt{Selling\:\:price=\bigg(\dfrac{100+5}{100}\bigg) \times 800}$

$\longrightarrow\tt{Selling\:\:price=\dfrac{105}{\cancel{100}}\times 8\cancel{00}}$

$\longrightarrow\tt{Selling\:\:price=Rs.(105 \times 8)}$

$\longrightarrow\bf{Selling\:\:price=Rs.840}$

$\underbrace{\bf{2^{nd}\:case\::}}$

• Cost price of other saree, (C.P) = Rs.800 .
• She sells other saree at on loss = 4%
• Sellin price = ?

Using formula of the selling price when show loss;

$\boxed{\bf{Selling\:price=\bigg(\frac{100-loss\%}{100} \bigg)\times C.P.}}$

$\longrightarrow\tt{Selling\:\:price=\bigg(\dfrac{100-4}{100}\bigg) \times 800}$

$\longrightarrow\tt{Selling\:\:price=\dfrac{96}{\cancel{100}}\times 8\cancel{00}}$

$\longrightarrow\tt{Selling\:\:price=Rs.(96 \times 8)}$

$\longrightarrow\bf{Selling\:\:price=Rs.768}$

Now;

Total cost price of both sarees = Rs.800 + Rs.800 = Rs.1600 .

Total selling price of both sarees = Rs.840 + Rs.768 = Rs.1608 .

C.P. < S.P.

As we know that formula of the profit :

$\mapsto\sf{Profit=Selling\:price-Cost\:price }$

$\mapsto\sf{Profit=Rs.1608-Rs.1600 }$

$\mapsto\sf{Profit=Rs.8 }$

$\boxed{\bf{Profit\:\% = \bigg(\frac{Profit}{C.P.} \times 100\bigg)\%}}$

$\mapsto\tt{Profit\:\% =\bigg( \dfrac{8}{16\cancel{00}} \times \cancel{100} \bigg)\%}\\\\\\\mapsto\tt{Profit\:\% = \bigg(\dfrac{8}{16} \bigg)\%}\\\\\\\mapsto\tt{Profit\:\% =\cancel{\dfrac{8}{16}}\%}\\\\\\\mapsto\tt{Profit\:\% = 1/2 \% }\\\\\mapsto\bf{Profit\:\% = 0.5\%}$

Thus;

The gain percent in the whole transaction will be 0.5% .