Question

A shopkeeper bought two fans for ₹ 5000 he sold one at a profit of 10%and the other at a loss of 10% if the SP of both the the fans are equal find the cost price of each fan

Answer 1

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The cost of one fan is Rs. 2250 and the cost of other fan is Rs. 2750.

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${\sf{\large{\underline{\pink{Given:}}}}}$

➛A shopkeeper bought two fans for ₹ 5000.

➛Sold one at a profit of 10%and the other at a loss of 10%.

➛The SP of both the the fans are equal.

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Cost price of each fan.

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We are given,

➛A shopkeeper bought two fans for ₹ 5000.

➛Sold one at a profit of 10%and the other at a loss of 10%.

➛The SP of both the the fans are equal.

Let the cost price of one fan be m.

Therefore, The cost price of other fan will be

Rs. ( 5000 - m ).

We know ,

${\green{\boxed{\pink{\star{\rm{Profit \ percent = \dfrac{P}{CP} \times 100}}}}}}$

${\implies{\rm{ 10 = \dfrac{P}{m} \times 100}}}$

${\implies{\rm{ P = \dfrac{m}{10} }}}$

so,

${\rm{SP\:of\:first\:fan = m + \dfrac{m}{10} }}$

${\rm{SP\:of\:first\:fan = \dfrac{11m}{10} }}$

. ............... ( since SP = CP + Profit )

We are given that he sold the other fan at 10% loss.

We know ,

${\green{\boxed{\pink{\star{\rm{Loss \ percent = \dfrac{L}{CP} \times 100}}}}}}$

${\implies{\rm{ 10 = \dfrac{L}{5000 - m} \times 100}}}$

${\implies{\rm{ L = \dfrac{5000 - m}{10} }}}$

so,

${\rm{SP\:of\: Second\:fan = ( 5000 - m ) - \dfrac{(5000 - m )}{10} }}$

. ............... ( since SP = CP - Loss)

According to given condition,

since, the SP of both fans is equal

${\implies{\rm{\dfrac{11m}{10} = ( 5000 - m ) - \dfrac{(5000 - m )}{10} }}}$

${\implies{\rm{\dfrac{11m}{10} = \dfrac{(5000 - 10m - 5000 + m )}{10} }}}$

${\implies{\rm{11m = 45000 - 9m}}}$

${\implies{\rm{11m + 9m = 45000 }}}$

${\implies{\rm{20m = 45000 }}}$

${\implies{\rm{m = \dfrac{45000}{20} }}}$

${\implies{\rm{m = 2250 }}}$

Hence cost price of first fan is Rs. 2250

now cost price of second fan,

= 5000 - 2250

= 2750

hence, cost price of second fan is RS. 2750.

Answer 2

Answer: Cost Price Of The First Fan is Rs.2750 And The Cost Price Of The Second Fan is Rs.2250.

Step-by-step explanation:

CP of both fans => Rs.5000

Let the first fan be x. Let the second fan be y.

Profit % of x => 10%

Loss % of y => 10%

SP of X = SP of Y

5000/2 = 2500

Let this be the base.

10% of 2500 = 10/100 * 2500

= 250.

Now, to find for x and y.

2500+250= Rs. 2750 (Profit of 10%)
2500-250= Rs. 2250 (Loss of 10%)

Hope this helped y'all! <33