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Word Problem 9 (Consecutive selling profits whats the cost?)

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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