Question

Bhawna bought two fans for Rs. 3605. She sold one at a profit of 15 % and the other at a loss of 9 %. If Bhawna obtained the same amount for each fan, find the cost price of each fan.​

Answer 1

★ Concept

This question is based on the concept of Profit and Loss. Understand the question first, Bhawna bought two fans for ₹ 3605 and what we are asked to calculate is the C.P (cost price) of each fans so we'll first assume the cost price of first fan be ₹ x thus, the cost price for the second fan would be ₹ (3605 - x). The first fan is sold at a profit of 15% while the second fan is sold at a loss of 9% so, with the help of formula we'll calculate first the S.P (selling price) of first and second fan. Bhawna obtained the same amount for each fan after selling them out (S.P of first fan will be equal to S.P of second fan). We will get an equation in terms of 'x' i.e the cost price for first fan and so does the cost price for second fan.

Let's proceed with Calculation !!

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Formula Used

${ \underline{{ \boxed{ \sf \orange{ S.P = \dfrac{100 + Profit \% }{100} \times C.P}}}}}$

${ \underline{{ \boxed{ \sf \orange{ S.P = \dfrac{100 - Loss \% }{100} \times C.P}}}}}$

[ Note : The above formula is a derivative for the general formula for calculating Profit and loss percentages].

Calculation

Let C.P. of first fan = ₹ x.

Then, C.P. of second fan = ₹(3605 - x)

For the sale of first fan, profit = 15 %

$\sf S.P_{first \: fan} = \dfrac{100 + 15}{100} x = \underline{\boxed{\red{ \rm\dfrac{115x}{100}}}}$

For the sale of second fan, loss = 9 %

$\sf S.P_{second \: fan} = \dfrac{100 - 9}{100} (3605 - x) = \underline{\boxed{\red{ \rm\dfrac{91(3605 - x)}{100}}}}$

✦ By the given condition,

S.P of first fan = S.P of second fan

$➺\rm \dfrac{115x}{100} = \dfrac{91(3605 - x)}{100}$

By Cross Multiplication,

⇒ 115x = 91(3605 - x)

⇒ 115x = 91 × 3605 - 91x

⇒ 115x + 91x = 91 × 3605

⇒ 206x = 91 × 3605

$\sf \: x = \dfrac{91 \times 3605}{206} = \dfrac{91 \times 35}{2}$

$\sf \: x \: = \dfrac{3185}{2} \qquad \rm x = 1592.50$

$\underline{ \boxed{ \bf \red{x \: = 1592.50}}}$

∴ C.P of first fan = ₹ x = ₹ 1592.50

[C.P of second fan = ₹ (3605 - 1592.50)]

C.P of second fan = ₹ 2012.50

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Additional Information

1) Cost price is the amount at which a shopkeeper buys his goods.

2) Selling price is the amount at which a shopkeeper sells his goods.

3) A profit is made when the selling price is greater than the cost price.

$\quad \sf Profit \: = S.P - C.P$

4) A loss is made when the selling price is less than the cost price.

$\quad \sf loss \: = C.P - S.P$

Answer 2

♦ concept

your question is asked on the basis of topic profit and loss. it is given that a girl bhawan bought two fans for ₹ 3605 she sold the first fan at the profit of 15% and unfortunately the second fan was sold at the loss of 9%. now we have to find the amount for each fan, also the cost price of each fan so simply. let the cost of first fan be ₹(x) and the cost of second fan be ₹ ( 3605 - x).

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♦ solution

⟹ let the C.P of first fan be ₹ X

⟹ then C.P. of second fan-Rs (3605-x)

⟹ for the sail of first fan, profit = 15%

⟹ S.P of first fan

$\: \sf \: :⟹ \frac{(100 + profit \: )}{100} \times C.P$

$\: \sf :⟹ ₹ \frac{(100 + 15)}{100} \times (x)$

$\: \sf :⟹ ₹\frac{115x}{100}$

⟹ For the sale of second fan, loss = 9%

⟹ S.P of second fan

$\sf :⟹ \frac{100 - loss}{100} \times C.P$

$\sf :⟹₹ \frac{100 - 9}{100} \times (3605 - x)$

$\sf :⟹₹ \frac{91(3605 - x)}{100}$

⟹ By the given condition,

⟹ S.P. of first fan = S.P. of second fan

$\sf \: ∴ \frac{115x}{100} = \frac{19(3605 - x)}{100}$

$\sf :⟹115x = 91(3605 - x) \: :⟹115x = 91 \times 3605 - 91x$

$\sf :⟹115x + 91x = 91 \times 3605:⟹206x = 91 \times 3605$

$\sf :⟹x = \frac{91 \times 3605}{206} = \frac{91 \times 35}{2} = \frac{3185}{2} = 1592.50$

$\sf :⟹ \sf \fbox \red{X = ₹1592.50}$

$\sf :⟹ \: C.P. \: of \: first \: fan = X = 1592.50$

$\sf :⟹ \: C.P. \: of \: second \: fan = ₹3605 - ₹1592.50 - ₹ 2012.50$

$\sf \fbox \red{:⟹₹ \: 2012.50}$

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♦ Note

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♦ Addictonal information

• Profit or Gain = Selling price – Cost Price

• Loss = Cost Price – Selling Price

• Profit percentage = (Profit /Cost Price) x 100

• Loss percentage = (Loss / Cost price) x 100

• Discount = cost Price – Selling Price

• Discount Percentage = (Discount/cost price) x 100