Question

10.Mr.Amit purchased a laptop for Rs.32000 and a phone for Rs.6500.On
On the laptop he lost 5% and on phone, he gained 15%. Find his total gain or loss %.

Answer 1

➤ Given :-

Cost price of laptop :- ₹32000

Cost price of phone :- ₹6500

Loss percentage of laptop :- 5%

Gain percentage of phone :- 15%

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➤ To Find :-

Total gain or loss percentage obtained to Amit.

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➤ Formula required :-

${\large \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{Profit \: (or) \: Loss}{CP} \times 100}}}}$

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★ How to do :-

Here, we are given with the cost price of a laptop and the loss percentage of that laptop. In the same question, we are given with the cost price of a phone and the gain percentage obtained of that phone. We are asked to find the total profit or loss percentage on the whole transaction. So, first we should find the selling price of both the gadgets by using the formula given below and then, we should find the total cost price and total selling price of both gadgets. Then, we should find the profit or loss. Later, we can use the given formula for finding the profit or loss percentage.

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➤ Solution :-

Selling price of laptop :-

${\tt \leadsto \dfrac{(100 - 5)}{100} \times 32000}$

${\tt \leadsto \cancel \dfrac{95}{100} \times 32000 = \dfrac{19}{20} \times 32000}$

${\tt \leadsto \dfrac{19}{\cancel{20}} \times \cancel{32000} = \dfrac{19}{1} \times 1600}$

${\tt \leadsto \dfrac{19 \times 1600}{1} = \dfrac{30400}{1}}$

${\tt \leadsto \cancel \dfrac{30400}{1} = 30400}$

Selling price of phone :-

${\tt \leadsto \dfrac{(100 + 15)}{100} \times 6500}$

${\tt \leadsto \cancel \dfrac{115}{100} \times 6500 = \dfrac{23}{20} \times 6500}$

${\tt \leadsto \dfrac{23}{\cancel{20}} \times \cancel{6500} = \dfrac{23}{1} \times 325}$

${\tt \leadsto \dfrac{23 \times 325}{1} = \dfrac{7475}{1}}$

${\tt \leadsto \cancel \dfrac{7475}{1} = 7475}$

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Total cost price :-

${\tt \leadsto 32000 + 6500}$

${\tt \leadsto Rs \: \: 38500}$

Total selling price :-

${\tt \leadsto 30400 + 7475}$

${\tt \leadsto Rs \: \: 37875}$

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Loss rupees :-

${\tt \leadsto 38500 - 37875}$

${\tt \leadsto Rs \: \: 625}$

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Now,

Loss percentage :-

${\tt \leadsto \dfrac{625}{38500} \times 100}$

${\tt \leadsto \dfrac{625}{\cancel{38500}} \times \cancel{100} = \dfrac{625}{385}}$

${\tt \leadsto \cancel \dfrac{625}{385} = \boxed{ \tt 1.62 \bf\%}}$

$\Huge\therefore$ The loss percentage on the whole transaction is 1.62%.

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$\dashrightarrow$ Some related formulas :-

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