Question

a shopkeeper bought two watch for rs.400. he sold them to gain 5% on one and loss 5% on the other. calculate his final gain or loss percent if the selling price of both watches are the same.​

Answer 1

➤ Given :-

Cost price of each watch :- ₹400

Gain percent of first watch :- 5%

Loss percent of second watch :- 5%

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➤ To Find :-

The overall gain or loss percentage.

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★ How to do :-

Here, we are given with the cost price of two watches. We are also given that one is sold at 5% of gain and the other watch is sold at 5% of loss. We are asked to find the total gain or loss percentage obtained to the shopkeeper while selling that watch. So, first we should find the selling price of both the watches. Then, we should find the profit or loss by subtracting the cost price and the selling price.

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➤ Solution :-

Selling price of first watch :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{(100 + Gain \bf\%)}{100} \times CP}}}$

Substitute the given values.

${\tt \leadsto \dfrac{(100 + 5)}{100} \times 400}$

First, add the given values in numerator.

${\tt \leadsto \dfrac{105}{100} \times 400}$

Write the given fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{105}{100} \times 400 = \dfrac{21}{20} \times 400}$

Write the denominator and the whole number in lowest form by cancellation method.

${\tt \leadsto \dfrac{21}{\cancel{20}} \times \cancel{400} = \dfrac{21}{1} \times 20}$

Now multiply the remaining numbers to get the selling price.

${\tt \leadsto \dfrac{21 \times 20}{1} = \underline{420}}$

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Now, find the selling price of the second watch.

Selling price of second watch :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{(100 - Gain \bf\%)}{100} \times CP}}}$

Substitute the given values.

${\tt \leadsto \dfrac{(100 - 5)}{100} \times 400}$

First, add the given values in numerator.

${\tt \leadsto \dfrac{95}{100} \times 400}$

Write the given fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{95}{100} \times 400 = \dfrac{19}{20} \times 400}$

Write the denominator and the whole number in lowest form by cancellation method.

${\tt \leadsto \dfrac{19}{\cancel{20}} \times \cancel{400} = \dfrac{19}{1} \times 20}$

Now multiply the remaining numbers to get the selling price.

${\tt \leadsto \dfrac{19 \times 20}{1} = \underline{380}}$

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Now, find the total cost price and also the total selling price of both watches.

Total cost price :-

${\tt \leadsto 400 + 400}$

${\tt \leadsto Rs \: \: 800}$

Total selling price :-

${\tt \leadsto 420 + 380}$

${\tt \leadsto Rs \: \: 800}$

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Now, solve for profit or loss rupees.

Profit or loss :-

${\tt \leadsto 800 - 800}$

${\tt \leadsto Rs \: \: 0}$

$\Huge\therefore$ The shopkeeper has neither obtained by profit nor loss.

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$\dashrightarrow$ Some related formulas :-

$\small\boxed{\begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\ \bigstar \: \sf{C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array}}$