Two items have a total cost of $225. Merchant mad 40% profit

Solution:

Let the CP of 1st item be \(x\). So, the CP of 2nd item \(= 225-x\).

We are told that the merchant made 40% profit from the sale of these two items. This means that profit earned from selling both the items \(=40\)% of \(225\).

\(⇒ \frac{40}{100} \times 225\)

\(⇒ 0.4\times 225\)

\(⇒ $90\).

Or SP of both the items \(= 225+90=$315\).

We are told that the merchant sells the first one at a profit of 25%. This means that profit earned from selling the 1st item \(=25\)% of \(x\).

\(⇒ \frac{25}{100} \times x\)

\(⇒ \frac{x}{4}\).

Or SP of 1st item \(= x+\frac{x}{4}=\frac{5x}{4}\).

Similarly, SP of 2nd item \(= 225-x + 50\)% of \((225-x) = 225-x + \frac{225-x}{2}=\frac{3(225-x)}{2}\).

So according to the problem:\( \frac{5x}{4}+\frac{3(225-x)}{2}=315\)

\(⇒ x=90\)

So the SP of 1st item \(= \frac{5x}{4}=\frac{5\times 90}{4}=112.5\)

And SP of 2nd item \(= \frac{3(225-x)}{2}=202.5\)

Hence the right answer is Option E.

Given: Two items have a total cost of $225. Merchant made 40% profit from the sale of these two items.
Asked: If the first item is sold on 25% profit and the second one on 50% profit, what is the selling price of the more expensive item?

Total Cost = $225
Profit = 40%
Total Selling Price = $225*1.4 = $315

Let the cost of one item be x.
Cost of another item = $225-x

Total Selling price = 1.25x + 1.5(225-x) = 225*1.4
22.5 = .25x
x = 90
225-x = 135

Cost of more expensive item = $135
Selling price of more expensive item = 1.5*$135 = $202.5

IMO E