Word problem 4_

Problem 4: A manufacturer sales a product to a whole sale dealer at 20% profit. The whole sale dealer sales the product to a retailer at 15% profit. The retailer sales the product to a customer in Rs 897 with 30% profit. What is the making cost of the manufacturer?

Solution:

Manufacturer

Let’s suppose cost price of manufacturer is ‘x’

i-e $CP = x$

It is given that manufacturer’s profit is 20% of cost price;

i-e $P= \frac{20}{100} of CP$

$\Rightarrow P= \frac{20}{100} \times x$

$\Rightarrow P= \frac{20}{100} \ x$

Now using formula for sale price;

$SP=P+CP$

$SP=\frac{20}{100}x+x$

$\Rightarrow SP=\frac{20x+100x}{100}$

$\Rightarrow SP=\frac{120x}{100}$

Whole Sale Dealer

Now this will become CP for whole sale dealer ;

$\Rightarrow CP=\frac{120x}{100}$

now wsd will earn 15% profit on his this CP;

i-e

$\Rightarrow P=15% of\frac{120x}{100}$

$\Rightarrow P=\frac{15}{100} \times(\frac{120x}{100})$

$\Rightarrow P=\frac{18x}{100}$

Again using formula for SP (for whole sale dealer);

$SP=P+CP$

$SP=\frac{18x}{100}+\frac{20x}{100}$

$SP=\frac{138x}{100}$

Retailer

Now this SP of whole sale dealer will become CP of retailer;

$\Rightarrow CP=\frac{138x}{100}$

Retailer earns 30% profit on this CP;

$\Rightarrow P= \frac{30}{100} of (\frac{138x}{100})$

$\Rightarrow P= \frac{30}{100} \times (\frac{138x}{100})$

$\Rightarrow P= \frac{207x}{500}$

Now again for sale price use;

$SP=P+CP$

$\Rightarrow SP= \frac{207x}{500}+ \frac{138x}{100}$

But given in question;

$Retailer's SP= Rs 897$

$\Rightarrow 897= \frac{207x}{500}+ \frac{138x}{100}$

$\Rightarrow 897= \frac{897x}{500}$

$\Rightarrow x= \frac{897\times 500}{897}$

$\Rightarrow x= RS 500$

So CP of manufacturer is 500 Rs.

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