Question

A shopkeeper bought two fans for rupees 5000 he sold one at 10% profit and one at 10% loss if SP of both the fans is equal find the CP of each fan ​

Answer 1

Answer:

Step by step explanation:

First formula :CP1+CP2=5000

Second formula:

Sp1 = CP1 + 0.1/10%CP1

Sp2= CP2 - 0.1/10% CP2

Since Sp1 = Sp2

CP1 + 0.1 CP1 = CP2 - 0.1 CP2

CP1 = 5000 - CP2

5000 - CP2 + 0.1 * 5000 - 0.1 CP2 = CP2 - 0.1 CP2

5500 = 2CP2

CP2 = 2750 rs

CP1 = 5000 - 2750

CP1 = 2250 rs

I hope it is helpful

Answer 2

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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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${\sf{\large{\underline{\blue{To \ Find}}}}}$

Cost price of each fan.

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${\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Solution:}}}}}}}}}$

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.