Manufacturer sells an article to a wholesaler at a profit of 18%. The wholesaler sells it to a retailer at a profit of 20%. The retailer sells to a customer at a profit of 25%. If the customer pays Rs.30.09 for it, ____ the cost of the manufacturer.

Question

Accepted Answer

Let the cost price for the article for the manufacturer is Rs.x
Now the manufacturer sold the article at a profit of 18% to the wholesaler.
We know,

SP = CP (\frac{100 + Profit %}{100})

\Rightarrow SP = x (\frac{100 + 18}{100})

\Rightarrow SP = \frac{118}{100} x

\Rightarrow SP = \frac{59}{50} x

Hence the selling price for the manufacturer is Rs.

\frac{59}{50} x

which becomes the cost price for the wholesaler. So, CP for wholesaler is Rs.

\frac{59}{50} x

.
Now, wholesaler sold it to retailer at a profit of 20% so,

SP = CP (\frac{100 + Profit %}{100})

\Rightarrow \frac{59}{50} x (\frac{100 + 20}{100})

\Rightarrow \frac{59}{50} x \times \frac{120}{100}

\Rightarrow Rs . \frac{354}{250} x

= Rs . \frac{177}{125} x

Hence the selling price for wholesalers is

Rs . \frac{177}{125} x

which becomes the cost price for the retailer. So,
CP for the retailer is

Rs . \frac{177}{125} x

The retailer sold the article to the customer at a profit of 25% so,

SP = CP (\frac{100 + Profit %}{100})

\Rightarrow \frac{177}{125} x (\frac{100 + 25}{100})

\Rightarrow \frac{177}{125} x \times \frac{125}{100}

\Rightarrow Rs . \frac{177}{100} x

So the selling price for the retailer becomes

Rs . \frac{177}{100} x

which becomes the cost price for the customer.
Hence, the cost price for the customer becomes

Rs . \frac{177}{100} x

We are given the cost price for customer as Rs.30.09 so, both the value will be equal,

Rs . \frac{177}{100} x

=30.09
Writing 30.09 as

\frac{3009}{100}

we get

\frac{177}{100} x = \frac{3009}{100}

177x = 3009.
Dividing both sides by 177, we get

x = \frac{3009}{177} = 17 .

Hence the value of x is 17.
Since x was supposed to be the cost price for the manufacturer. So our required answer is Rs.17

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