Practice | Hashtable

Home > Practice > Arithmetic Aptitude > True Discount > Miscellaneous

1. An article of cost price Rs. 8000 is marked at Rs. 11200, after allowing a discount of x percent a profit of 12% is made. The value of x is = ?

A. 21%

B. 20%

C. 22%

D. 23%

Solution:

Cost price of the article = Rs. 8000
Profit% = 12%
Selling price of the article

\begin{aligned} =  Cost price \times \frac{100 + P %}{100} \\ = 8000 \times \frac{112}{100} \\ =  Rs . 8960 \end{aligned}

\begin{aligned} ∴ Discount \\ =  Marked price - Selling price \\ = 11200 - 8960 \\ =  Rs . 2240 \end{aligned}

Let the discount percentage = x%

\begin{aligned} ∴ \frac{11200 \times x}{100} = 2240 \\ \Rightarrow x = \frac{2240 \times 100}{11200} \\ \Rightarrow x = 20 % \end{aligned}

Alternate :

\begin{aligned} \frac{100 - D %}{100 + P %} = \frac{Cost price}{Marked price} \\ \Rightarrow \frac{100 - x}{100 + 12} = \frac{5}{7} \\ \Rightarrow \frac{100 - x}{112} = \frac{5}{7} \\ \Rightarrow 700 - 7 x = 560 \\ \Rightarrow 7 x = 700 - 560 \\ \Rightarrow x = \frac{140}{7} \\ \Rightarrow x = 20 % \end{aligned}

You must login to add comments. Login now.