Question

a Man gains 12*1/2% by selling a house for ₹4500. find his gain percent And loss percent if he sells the house for₹3800​

Answer 1

Step-by-step explanation:

gain=25/2%

selling price=4500

cost price= 4500*100/(100+25/2)

=4500*100/(225/2)

=4000

new selling price=3800

loss=200

loss%= 200*100/4000=5%

Answer 2

➤ Given :-

Selling price of house :- ₹4500

Gain percentage :- 12½%

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➤ To Find :-

The profit or loss percentage if sold at ₹3800.

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★ How to do :-

Here, we are given with the selling price and the gain percentage obtained while selling that house. In the other statement, we are given that the house is again sold at ₹3800. We are asked to find the gain ir loss percentage obtained at the second statement. So, first we should find the cost price of that house by using the information in first statement. The particular formula is given when the question has been solved. Later, we should find the loss rupees by subtracting the cost price and the selling price. Later, we can find the loss percentage by using the given formula while solving.

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➤ Solution :-

Cost price of the house :-

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

Substitute the given values.

${\tt \leadsto \dfrac{100}{(100 + 12.5)} \times 4500}$

Solve the bracket given in denominator.

${\tt \leadsto \dfrac{100}{112.5} \times 4500}$

Write the fraction a bit larger format, in which it's value doesn't changes.

${\tt \leadsto \dfrac{1000}{1125} \times 4500}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \dfrac{1000}{\cancel{1125}} \times \cancel{4500} = \dfrac{1000}{1} \times 4}$

Now multiply both numbers as it cannot be cancelled.

${\tt \leadsto \cancel \dfrac{1000 \times 4}{1} = \underline{4000}}$

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Now, find the loss by using the formula given below.

Loss rupees :-

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

Substitute the given values.

${\tt \leadsto 4000 - 3800}$

Subtract to get the value of loss.

${\tt \leadsto \underline{Rs \: \: 200}}$

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Now, find the loss percentage by using the formula given below.

Loss percentage :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{Loss}{CP} \times 100}}}$

Substitute the given values.

${\tt \leadsto \dfrac{200}{4000} \times 100}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{200}{4000} \times 100 = \dfrac{1}{20} \times 100}$

Now, multiply the numbers as they cannot be cancelled further.

${\tt \leadsto \dfrac{1 \times 100}{20} = \dfrac{100}{20}}$

Write the fraction in lowest form to get the answer.

${\tt \leadsto \cancel \dfrac{100}{20} = \pink{\underline{\boxed{\tt 5 \bf\%}}}}$

$\Huge\therefore$ The loss percentage of the house is 5%.

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$\dashrightarrow$ Some related formulas :-

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