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A shopkeeper purchased $150$ identical pieces of calculators at the rate of $Rs . 250$ each. He spent an amount of $Rs . 2500$ on transport and packing. He fixed the labelled price of each calculator at $Rs . 320$ . However he decided to give a discount of $5 %$ on the labelled price. What is the percentage profit earned by him?

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14 %

15 %

16 %

20 %

answer is A.

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Detailed Solution

Given,
Number of pieces of calculator purchased = 150.
Rate of each piece = Rs.250.
Amount spent on packaging and transport = Rs.2500.
Labelled price of each calculator = Rs.320.
Discount percent on each labelled price = 5%.
We know,
Discount =

\frac{100 - Discount %}{100}

\Rightarrow

Discount =

\frac{100 - 5}{100}

\Rightarrow

Discount =

\frac{95}{100}

Then,
Cost of each calculator = Rate of each piece +

\frac{Total amount spend on packaging and transport}{Number of pieces}

Cost of each calculator =

250 + \frac{2500}{150}

\Rightarrow

Cost of each calculator

= 250 + \frac{50}{3}

\Rightarrow

Cost of each calculator

= \frac{750 + 50}{3}

\Rightarrow

Cost of each calculator

= Rs . \frac{800}{3}

Now,
S.P of each calculator =

Discount \times Labelled price

\Rightarrow

S.P of each calculator =

\frac{95}{100} \times 320

\Rightarrow

S.P of each calculator

= Rs . 304

We know,
Profit = SP - CP

\Rightarrow

Profit =

304 - \frac{800}{3}

\Rightarrow

Profit =

\frac{912 - 800}{3}

\Rightarrow

Profit =

Rs . \frac{112}{3}

Then,
Profit Percentage =

\frac{profit}{CP} \times 100

\Rightarrow

Profit Percentage =

\frac{112}{3} \times \frac{3}{800} \times 100

\Rightarrow

Profit Percentage= 14%
Thus, the profit percent is 14%.
Therefore, the correct option is 1.

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