NIMCET 2024 — Reasoning PYQ

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Question

NIMCET 2024 — Reasoning PYQ

NIMCET | Reasoning | 2024

After allowing 20% cash discount, a trader still earns a profit of 11.11%. How much above the cost price, the trader marks his goods ?

Choose the correct answer:

Explanation

1. Given Data:

Discount ( $D$ ) = $20\%$
Profit ( $P$ ) = $11.11\%$

In fractional form:

$20\% = \frac{1}{5}$
$11.11\% = \frac{1}{9}$

2. Relationship Formula:

The ratio of Marked Price to Cost Price is given by:

\frac{MP}{CP} = \frac{100 + \text{Profit}\%}{100 - \text{Discount}\%}

3. Calculation:

Substituting the percentages:

\frac{MP}{CP} = \frac{100 + 11.11}{100 - 20}

\frac{MP}{CP} = \frac{111.11}{80}

To simplify, we can use the fractional equivalents ( $1 + \frac{1}{9}$ for profit and $1 - \frac{1}{5}$ for discount):

\frac{MP}{CP} = \frac{\frac{10}{9}}{\frac{4}{5}}

\frac{MP}{CP} = \frac{10}{9} \times \frac{5}{4} = \frac{50}{36} = \frac{25}{18}

4. Finding the Markup Percentage:

The Markup is the difference between $MP$ and $CP$ :

\text{Markup} = MP - CP = 25 - 18 = 7

\text{Markup}\% = \left( \frac{\text{Markup}}{CP} \right) \times 100

\text{Markup}\% = \left( \frac{7}{18} \right) \times 100

\text{Markup}\% = 38.88\%

Correct Option:

C) 38.88%