Question

Q. A shopkeeper sold two Electric guitars for rupees
88000 each. The Shopkeeper made a loss of 12% on one
and a profit of 10% on the other. Find his overall gain or
loss.​

Answer 1

$\underline{ \underline{ \Large \sf { \purple{Given:}} } }$

• A shopkeeper sold two electric guitars for rupees 88000 each.

• The Shopkeeper made a loss of 12% on one and a profit of 10% on the other.

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$\underline{ \underline{ \Large \sf { \pink{To \: calculate:}} } }$

• His overall gain or loss.

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$\underline{ \underline{ \Large \sf { \blue{Calculation:}} } }$

Here, we are given that the selling price of two electric guitars is Rs. 88000 each. Also, the shopkeeper got 12 % loss on first guitar and 10 % profit on the second guitar. In order to tackle this question i.e, to his overall gain or loss , we have to find total selling price and cost price in the whole transaction.

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Case I :

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✰ Selling price of the guitar = Rs. 88000

✰ Loss % = 12 %

Let's find out the cost price of the first guitar. We know that the value of cost price when selling price and loss % are given is represented by given below formula :

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$\: \: \: \: \: \: \: \longrightarrow \boxed{ \pmb{ \rm \gray{C.P = \dfrac{100}{100- Loss \: \%} \times S.P }}}$

Now, inserting the given values in the formula to find C.P.

$\\ \longrightarrow \sf{C.P =Rs. \bigg \lgroup \dfrac{100}{100 - 12} \times 88000 \bigg \rgroup} \\ \\ \\ \longrightarrow \sf{C.P =Rs. \bigg \lgroup \dfrac{100}{88} \times 88000 \bigg \rgroup} \\ \\ \\ \longrightarrow \sf{C.P =Rs. \lgroup 100 \times 1000 \rgroup } \\ \\ \\ \longrightarrow \sf{C.P =Rs. \: 100000 }$

Henceforth,

• Cost price of the first guitar is Rs. 100000.

Case II :

Now, let's find out the cost price of the second guitar.

We know that the value of cost price when selling price and profit % are given is represented by given below formula :

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$\: \: \: \: \: \: \: \longrightarrow \boxed{ \pmb{ \rm \gray{C.P = \dfrac{100}{100 + Profit \: \%} \times S.P }}}$

Now, inserting the given values in the formula to find C.P.

$\\ \longrightarrow \sf{C.P =Rs. \bigg \lgroup \dfrac{100}{100 + 10} \times 88000 \bigg \rgroup} \\ \\ \\ \longrightarrow \sf{C.P =Rs. \bigg \lgroup \dfrac{100}{110} \times 88000 \bigg \rgroup} \\ \\ \\ \longrightarrow \sf{C.P =Rs. \bigg \lgroup \dfrac{8800000}{110} \bigg \rgroup } \\ \\ \\ \longrightarrow \sf{C.P =Rs. \: 80000 }$

Henceforth,

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Cost price of the second guitar is Rs. 80000.

Therefore,

$\longrightarrow \sf {{Cost \: price}_{[Both \: guitars]} = {Cost \: price}_{[First \: guitar]} + {Cost \: price}_{[Second \: guitar]} } \\ \\ \\ \longrightarrow \sf {{Cost \: price}_{[Both \: guitars]} = Rs. \: ( 100000+ 80000) } \\ \\ \\ \longrightarrow \sf {{Cost \: price}_{[Both \: guitars]} = Rs. \: 176000}$

Also,

$\longrightarrow \sf {{Selling \: price}_{[Both \: guitars]} = {Selling \: price}_{[First \: guitar]} + {Selling \: price}_{[Second \: guitar]} } \\ \\ \\ \longrightarrow \sf {{Selling \: price}_{[Both \: guitars]} = Rs. \: ( 88000+ 88000) } \\ \\ \\ \longrightarrow \sf {{Selling \: price}_{[Both \: guitars]} = Rs. \: 180000}$

Clearly, we can observe that here selling price is greater than the cost price. Also , whenever there is selling price greater than cost price, there is gain and gain is calculated by subtracting cost price from the selling price. So,

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$\: \: \: \: \: \: \: \longrightarrow \boxed{ \pmb{ \rm \gray{Gain = Selling \: price - Cost \: price }}} \\ \\ \\ \longrightarrow \sf { Rs. \: ( 180000 - 176000) } \\ \\ \\ \longrightarrow \boxed { \pmb {\rm \red{Gain = Rs. \: 4000}}}$

Therefore,

• His overall gain is $\pmb {\mathfrak \gray{Rs. \: 4000} }$

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