f the selling price of an article is five times the discount offered and if the percentage of discount isequal to the percentage profit, what is the ratio of the discount offered to the cost price?(a) 11 : 30 (b) 4 : 15 (c) 7 : 30 (d) 1 : 6 (e) 3 : 25
Question
f the selling price of an article is five times the discount offered and if the percentage of discount isequal to the percentage profit, what is the ratio of the discount offered to the cost price?(a) 11 : 30 (b) 4 : 15 (c) 7 : 30 (d) 1 : 6 (e) 3 : 25
Solution
To solve this problem, let's assume the cost price of the article is x.
According to the given information, the selling price of the article is five times the discount offered. So, the selling price can be expressed as 5 times the discount, which is 5x.
It is also given that the percentage of discount is equal to the percentage profit. Let's assume this percentage to be y.
The discount offered can be calculated as y% of the cost price, which is (y/100) * x.
Since the selling price is equal to the cost price minus the discount, we can write the equation as:
5x = x - (y/100) * x
Simplifying the equation, we get:
5x = x(1 - y/100)
Dividing both sides by x, we have:
5 = 1 - y/100
Rearranging the equation, we get:
y/100 = 1 - 5
y/100 = -4
Now, let's find the ratio of the discount offered to the cost price:
Discount offered = (y/100) * x
Ratio = (y/100) * x / x
Simplifying, we get:
Ratio = y/100
Therefore, the ratio of the discount offered to the cost price is y/100.
Since we have found that y/100 = -4, the ratio is -4/100, which simplifies to -1/25.
However, ratios are typically expressed in positive terms. So, we can multiply both the numerator and denominator by -1 to get a positive ratio.
Therefore, the ratio of the discount offered to the cost price is 1/25.
None of the given answer choices match this ratio, so none of the options (a), (b), (c), (d), or (e) are correct.
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