Question

A Horse and a Cow were sold for Rs. 12000/ each. The horse was sold at a loss of 20% and the Cow at a gain
of 20%. Find his overall gain or loss.
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Answer 1

➤ Given :-

Selling price of horse :- ₹12000

Selling price of cow :- ₹12000

Loss percent of horse :- 20%

Gain percent of cow :- 20%

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➤ To Find :-

The overall gain or loss rupees obtained.

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★ How to do :-

Here, we are given with the selling price of a horse and a selling price of a cow. We are also given with the gain and loss percentage obtained for the same. We are asked to find the total profit or loss rupees obtained for both animals together. We use three formulas in this whole question. We need two formulas to find the selling price and one formula to find the profit or loss percentage. The appropriate formulas are provided while solving the problems. The related formulas are given at last. So, let's solve!!

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➤ Solution :-

Cost price of horse :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{100}{(100 - Loss \bf\%)} \times SP}}}$

Substitute the given values.

${\tt \leadsto \dfrac{100}{(100 - 20)} \times 12000}$

Firstly, subtract the values in denominator and write the fraction in lowest form.

${\tt \leadsto \cancel \dfrac{100}{80} \times 12000 = \dfrac{5}{4} \times 12000}$

Multiply the remaining numbers.

${\tt \leadsto \dfrac{5 \times 12000}{4} = \dfrac{60000}{4}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{60000}{4} = 15000}$

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Cost price of cow :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{100}{(100 + Profit \bf\%)} \times SP}}}$

Substitute the given values.

${\tt \leadsto \dfrac{100}{(100 + 20)} \times 12000}$

Firstly, add the values in denominator and write the fraction in lowest form.

${\tt \leadsto \cancel \dfrac{100}{120} \times 12000 = \dfrac{5}{6} \times 12000}$

Multiply the remaining numbers.

${\tt \leadsto \dfrac{5 \times 12000}{6} = \dfrac{60000}{6}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{60000}{6} = 10000}$

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Now, we should add both cost price separately and both selling price separately.

Total cost price:-

${\tt \leadsto 15000 + 10000}$

Add the values to get the total cost price.

${\tt \leadsto Rs \: \: 25000}$

Total selling price :-

${\tt \leadsto 12000 + 12000}$

Add the values to get the total cost price.

${\tt \leadsto Rs \: \: 24000}$

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Here, we can see that the cost price is greater than the selling price. So, we are obtained with the loss. So,

Loss rupees :-

${\tt \leadsto \underline{\boxed{\sf Cost \: price - Selling \: price}}}$

Substitute the given values.

${\tt \leadsto 25000 - 24000}$

Subtract the values to get the answer.

${\tt \leadsto Rs \: \: 1000}$

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${\red{\underline{\boxed{\bf So, \: the \: loss \: of \: whole \: transaction \: is \: \: Rs.1000}}}}$

Answer 2

Question :-

A Horse and a Cow were sold for Rs. 12000/ each. The horse was sold at a loss of 20% and the Cow at a gain

of 20%. Find his overall gain or loss.

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Solution :-

Given Information :-

• Selling price of horse = ₹12000
• Selling price of cow = ₹12000
• Loss percent of horse = 20%
• Gain percent of cow = 20%

To Find :-

The overall gain or loss in the whole transaction.

Calculation :-

• Cost price of horse :-

${\sf : \implies \sf \dfrac{100}{(100 - Loss \%)} \times SP}$

Substituting the given values, We get,

$\sf: \implies{\sf \dfrac{100}{(100 - 20)} \times 12000}$

$\sf : \implies \dfrac{100}{80} \times 12000$

Cancelling 100 and 80, We get,

$: \implies{\sf \dfrac{5}{4} \times 12000}$

$:\implies{\sf \dfrac{60000}{4}} = \sf15000$

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• Cost price of cow :-

$: \implies{\sf{\sf \dfrac{100}{(100 + Profit \bf\%)} \times SP}}$

Substituting the given values, We get,

$: \implies{\sf \dfrac{100}{(100 + 20)} \times 12000}$

$: \implies{\sf\dfrac{100}{120} \times 12000}$

Cancelling 100 and 120, We get,

$\sf: \implies 10 \times 1000$

$\sf: \implies 10000$

Now, Adding both Cost Price separately and both selling price separately, We get,

Total cost price:-

$\sf: \implies{\sf 15000 + 10000 =Rs. \: 25000}$

Total selling price :-

$\sf: \implies 12000 + 12000 =Rs. \: 24000$

∵ The cost price is greater than the selling price.

∴ Loss takes place,

• Loss rupees :-

∵ Loss = Cost Price - Selling Price.

Substituting the values, We get,

${\sf:\implies 25000 - 24000}$

${\sf: \implies Rs.\: 1000}$

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Final Answer :-

The loss of complete transaction process is Rs. 1000

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