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%
Answer: Option B
Solution(By Examveda Team)
Cost price of the article = Rs. 8000Profit% = 12%
Selling price of the article
$$\eqalign{ & {\text{ = Cost price}} \times \frac{{100 + {\text{P}}\% }}{{100}}{\text{ }} \cr & = 8000 \times \frac{{112}}{{100}} \cr & {\text{ = Rs}}{\text{. 8960}} \cr} $$
$$\eqalign{ & \therefore {\text{ Discount }} \cr & {\text{ = Marked price}} - {\text{Selling price}} \cr & {\text{ = 11200}} - {\text{8960 }} \cr & {\text{ = Rs}}{\text{. 2240}} \cr} $$
Let the discount percentage = x%
$$\eqalign{ & \therefore \frac{{11200 \times x}}{{100}} = 2240 \cr & \Rightarrow x = \frac{{2240 \times 100}}{{11200}} \cr & \Rightarrow x = 20\% \cr} $$
Alternate :
$$\eqalign{ & \frac{{100 - {\text{D}}\% }}{{100 + {\text{P}}\% }} = \frac{{{\text{Cost price}}}}{{{\text{Marked price}}}} \cr & \Rightarrow \frac{{100 - x}}{{100 + 12}} = \frac{5}{7} \cr & \Rightarrow \frac{{100 - x}}{{112}} = \frac{5}{7} \cr & \Rightarrow 700 - 7x = 560 \cr & \Rightarrow 7x = 700 - 560 \cr & \Rightarrow x = \frac{{140}}{7} \cr & \Rightarrow x = 20\% \cr} $$
Related Questions on True Discount
The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:
A. 12%
B. 13%
C. 15%
D. 14%
A. Rs. 9025.20
B. Rs. 9200
C. Rs. 9600
D. Rs. 9560
A. Rs. 12,000 in cash
B. Rs. 12,880 at credit
C. Both are equally good
D. Rs. 18.33
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