Word Problem 9

Profit & Loss 0

Problem 9: A sold a table to B at 4% profit.B sold the same table for Rs 65, thereby he made a profit of 25%. Find the price at which A had purchased the table.

a. 40 b.60. c.50 d.70

Solution:

Let the cost price for A is Rs ‘y’. A earns a profit of 4% of his cost price

i-e

$A's Profit=\frac{4}{100} of 'y'$

$=\frac{4y}{100}$

$=\frac{y}{25}$

But

$Profit= Sale Price - Cost Price$

$\Rightarrow \frac{y}{25} = SP-y$

$\Rightarrow SP=\frac{y}{25}+y$

$=\frac{26y}{25}$

So, the sale price at which A sold table to B is 26y/25. So, now it will stand as cost price for B.

Now we consider B’s case

Cost price of B

$CP=\frac{26y}{25}$

Sale price by B at which he sold table is Rs. 65 i-e

$SP=65$

Profit earned by B is 25% of his cost price i-e

$P=\frac{25}{100} of CP$

$=\frac{1}{4} \times \frac{26y}{25}$

But

$Profit=Sale Price-Cost Price$

or

$P=SP-CP$

Putting values of P, SP, CP

$\Rightarrow\frac{1}{4}\times\frac{26y}{25}=65-\frac{26y}{25}$

$\Rightarrow\frac{1}{4} \times \frac{26y}{25}+\frac{26y}{25}=65$

$\Rightarrow\frac{5}{4} \times \frac{26y}{25}=65$

$\Rightarrow y=\frac{4}{5} \times \frac{25}{26}\times65$

$\Rightarrow y=50$

So the cost price by A was Rs 25

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