Question

A dealer sold two machines at Rupees 2400 each.On selling one machine,he gained 20%and on the other hand he lost 20%.Find the dealer's net gain or loss per cent.​

Answer 1

➤ Given :-

Selling price of each machines :- ₹ 2400

Profit percentage of one machine :- 20%

Loss percentage of one machine :- 20%

➤ To Find :-

Total gain or loss percentage to the dealer

➤ Formulas required :-

Cost price of one machine :-

${\large \tt \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{100 \times SP}{100 + Profit \: \bf\%}}}}}$

Cost price of one machine :-

${\large \tt \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{100 \times SP}{100 - Loss \: \bf\%}}}}}$

➤ Solution :-

First, we should find the cost price of both machines by using the given formulas

Cost price of first machine :-

${\tt \longrightarrow \dfrac{100 \times 2400}{100 + 20}}$

${\tt \longrightarrow \dfrac{100 \times \cancel{2400}}{\cancel{120}} = \dfrac{100 \times 20}{1}}$

${\tt \longrightarrow 100 \times 20 = \boxed{\tt Rs \: \: 2000}}$

Cost price of second machine :-

${\tt \longrightarrow \dfrac{100 \times 2400}{100 - 20}}$

${\tt \longrightarrow \dfrac{100 \times \cancel{2400}}{\cancel{80}} = \dfrac{100 \times 30}{1}}$

${\tt \longrightarrow 100 \times 30 = \boxed{\tt Rs \: \: 3000}}$

Now, we have found the cost price of both the machines, so we should find the profit and loss in numerical format

Profit of first machine :-

${\tt \longrightarrow 2400 - 2000}$

${\tt \longrightarrow Rs \: \: 400}$

Loss of second machine :-

${\tt \longrightarrow 3000 - 2400}$

${\tt \longrightarrow Rs \: \: 600}$

So, here the loss is greater than profit

So,

Total loss percentage :-

${\tt \longrightarrow \dfrac{600 - 400}{5000} \times 100}$

${\tt \longrightarrow \dfrac{200}{\cancel{5000}} \times \cancel{100} = \dfrac{200}{50}}$

${\tt \longrightarrow \cancel \dfrac{200}{50} = \boxed{\tt 4 \bf\%}}$

$\Huge\therefore$ The net loss percentage of the machines is 4%.

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More to know :-

• Profit and loss are obtained for all shopkeepers in their shops. The profit is obtained when the selling price is greater than cost price. The loss is obtained when the cost price is greater than selling price. The profit and loss can also be converted into percentage format by some mathematical formulas.
• To convert the profit to percentage from, first we should divide the profit and cost price and then multiply by 100.
• To convert the loss to percentage form, first we should divide the loss and cost price and then multiply by 100.

Answer 2

Given:

• A dealer sold two machines at Rupees 2400 each.
• On selling one machine,he gained 20%and on the other hand he lost 20%

To Find:

• The dealer's net gain or loss per cent..

Formulas used:

• $\bf \: C.P. \: = \bigg( \dfrac{S.P. \times 100}{100 \: + \: gain\% } \bigg)$

• $\bf \: C.P. \: = \bigg( \dfrac{S.P. \times 100}{100 \: - \: loss\% } \bigg)$

• $\bf \: Loss = \bigg(\dfrac{Loss }{ Cost \: price} \bigg)\times 100\%$

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First Machine:

S.P. = ₹ 2400 and gain% = 20%

$\therefore \: \: \: \: \: \: \: \: \: \sf \: C.P. \: = \bigg( \dfrac{S.P. \times 100}{100 \: + \: gain\% } \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{2400\times 100}{100 + 20} \bigg) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= \: ₹ \: \bigg( \dfrac{2400 \times 10 \cancel0}{12 \cancel0} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{2400 \times 10}{12} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{ \cancel{2400 0}}{{ \cancel{1 2}}} \bigg) \\ \\ \: \: \: \: \: \: \sf= ₹ { \underline{ \boxed{ \bf{ \bigstar{ \pink{2000}}}}}}$

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Second Machine:

S.P. = ₹ 2400 and loss% = 20%

$\therefore \: \: \: \: \: \: \: \: \: \sf \: C.P. \: = \bigg( \dfrac{S.P. \times 100}{100 \: - \: loss\% } \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{2400 \times 100}{100 - 20} \bigg) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= \: ₹ \: \bigg( \dfrac{2400 \times 10 \cancel0}{8 \cancel0} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{2400 \times 10}{8} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \sf= ₹ \: \bigg( \dfrac{ \cancel{2400 0}}{{ \cancel{8}}} \bigg) \\ \\ \: \: \: \: \: \: \sf= ₹ { \underline{ \boxed{ \bf{ \bigstar{ \pink{3000}}}}}}$

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Hence, Total cost price of two machines:

• ₹ (2000 + 3000 ) = ₹ 5000

⠀

Total selling price of two machines:

• ₹ (2400 × 2) = ₹ 4800

⠀

Since, C.P. > S.P., There is a loss.

• Loss = ₹ (5000 – 4800) = ₹200

So,

$\therefore\sf \: \: \: \: \: \: Loss = \bigg(\dfrac{Loss }{ Cost \: price} \bigg)\times 100\% \\ \\ \sf \:➟ \: \: \:Loss = \bigg(\dfrac{200 }{ 5000} \bigg)\times 100\% \: \: \:\\ \\ \sf➟ \: \: \: \: Loss = \bigg(\dfrac{200 }{ 50 \cancel{00} } \bigg)\times 1 \cancel{00}\% \: \: \: \: \: \: \\ \\ \sf \: \therefore \: \: \: \: \: \: \: \: Loss \: = \frac {200}{50}\: = 4\%$

⠀⠀Hence, Loss percent is 4%