Question

20 C.P. ol 30 articles – S.P. ol 40 arucles.
6.
Mukesh bought 50 dozen ball pens and sold 20 dozens at a profit of 12%, 25 dozens at
a profit of 15% and the remaining 5 dozens at a loss of 10%. If the total selling price
was? 6678. find the cost price of one dozen of ball pens and the percentage of profit
earned on the whole transaction.
​

Answer 1

Given:

Mukesh bought 50 dozen ball pens

Mukesh sold 20 dozens at a profit of 12%, 25 dozens at  a profit of 15% and the remaining 5 dozens at a loss of 10%

If the total selling price  was Rs. 6678

To find:

Find the cost price of one dozen of ball pens and the percentage of profit earned on the whole transaction

The formula used to solve the problem:

$\boxed{\bold{S.P. = \frac{100 + G\%}{100} \times C.P.}}\\\\\boxed{\bold{S.P. = \frac{100 - L\%}{100} \times C.P.}}$

Solution:

Let "x" represent the C.P. of 1 dozen ball pens.

According to the question and using the formula above, we can write the equation to find the total selling price of the articles as follows:

[S.P. of 20 dozens] + [S.P. of 25 dozens] + [S.P. of 5 dozens] = [Total S.P. of 50 dozen ball pens]

$\implies [(\frac{100 + 12}{100})x ]20 \:+\: [(\frac{100 + 15}{100})x ]25 \:+\: [(\frac{100 - 10}{100})x ]5 = 6678$

$\implies [(\frac{112}{100})x ]20 \:+\: [(\frac{115}{100})x ]25 \:+\: [(\frac{90}{100})x ]5 = 6678$

$\implies [1.12x ]20 \:+\: [1.15x ]25 \:+\: [0.9x ]5 = 6678$

$\implies 22.4x \:+\: 28.75x \:+\: 4.5x = 6678$

$\implies 55.65x = 6678$

$\implies x = \frac{6678}{55.65}$

$\implies \bold{x = 120}$ ← C.P. of 1 dozen ball pens

∴ C.P. of 50 dozen ball pens = Rs. 120 × 50 = Rs. 6000

∵ [Total S.P. of 50 dozens ball pens]  > [Total C.P. of 50 dozen ball pens]

⇔ Mukesh will earn a profit on the whole transaction

Now,

The profit percentage earned by Mukesh is,

= $\frac{S.P. \:-\: C.P. }{C.P.} \times 100$

= $\frac{6678 \:-\: 6000 }{6000} \times 100$

= $\frac{678 }{6000} \times 100$

= $0.113 \times 100$

= $\bold{11.3\:\%}$

Thus,

$\boxed{\boxed{\bold{ The\: cost\: price\: of\: one\: dozen\: of \:ball\: pens\: is \:\underline{Rs.\: 6000}.}}}\\\\and\\\\\boxed{\boxed{\bold{ The\: percentage\: of\: profit\:earned\: on\: the\: whole\: transaction\:is \:\underline{11.3\%}.}}}$

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