Question

If an item is sold for rs. 1080 at profit of 10%, then it's cp is ____________

Answer 1

Given :

Selling price = ₹1080

Profit % = 10 %

Find : Cost price

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METHOD 1 :

Formula to use :

$cp = \dfrac{100}{100 + p\%} \times sp$

$cp = \frac{100}{100 + 10} \times 1080$

$cp = \frac{100}{110} \times 1080$

by reducing to the lowest terms we get,

cp =

$981 \dfrac{9}{11}$

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METHOD 2 :

Let cp be x.

We know that,

Sp = Cp + profit

$profit = \dfrac{profit\%}{100} \times cp$

therefore,

$1080 = x + ( \frac{10}{100} \times x)$

$1080 = x + ( \frac{10x}{100} )$

$1080 = \frac{100x + 10x}{100}$

as LCM = 100

$1080 = \frac{110x}{100}$

by cross multiplication,

$1080 \times 100 = 110x$

$108000 = 110x$

$\frac{108000}{110} = x$

$x = 981 \frac{9}{11}$

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SOME MORE FORMULAS:

$cp = \frac{100}{100 - loss\%} \times sp$

$sp = \frac{100 + profit\%}{100} \times cp$

sp = {(100-loss%) ÷ 100} × cp

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Note : Sp - Selling price

Cp = Cost price.

______________________________________

Answer 2

Given :

Selling price = ₹1080

Profit % = 10 %

Find : Cost price

--------------------------------------------

METHOD 1 :

Formula to use :

cp = \dfrac{100}{100 + p\%} \times spcp=

100+p%

100

×sp

cp = \frac{100}{100 + 10} \times 1080cp=

100+10

100

×1080

cp = \frac{100}{110} \times 1080cp=

110

100

×1080

by reducing to the lowest terms we get,

cp =

981 \dfrac{9}{11}981

11

9

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METHOD 2 :

Let cp be x.

We know that,

Sp = Cp + profit

profit = \dfrac{profit\%}{100} \times cpprofit=

100

profit%

×cp

therefore,

1080 = x + ( \frac{10}{100} \times x)1080=x+(

100

10

×x)

1080 = x + ( \frac{10x}{100} )1080=x+(

100

10x

)

1080 = \frac{100x + 10x}{100}1080=

100

100x+10x

as LCM = 100

1080 = \frac{110x}{100}1080=

100

110x

by cross multiplication,

1080 \times 100 = 110x1080×100=110x

108000 = 110x108000=110x

\frac{108000}{110} = x

110

108000

=x

x = 981 \frac{9}{11}x=981

11

9

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SOME MORE FORMULAS:

cp = \frac{100}{100 - loss\%} \times spcp=

100−loss%

100

×sp

sp = \frac{100 + profit\%}{100} \times cpsp=

100

100+profit%

×cp

sp = {(100-loss%) ÷ 100} × cp

----------------------------------------------

Note : Sp - Selling price

Cp = Cost price.

______________________________________