A manufacturer of detergent cakes increased the price of his product a...
Let original price = Rs 100 No. of Units gold =100 Turn-over = Rs 10000 Now, No. of Units sold = 80 Turn-over = Rs 12000
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A manufacturer of detergent cakes increased the price of his product a...
Increase in price and decrease in sales
Let's assume the original price of the detergent cake is P and the original sales turnover is T.
According to the question, there was a decrease of 20% in the sales turnover when the price increased.
So, the new sales turnover is (1 - 0.2)T = 0.8T.
Increase in sales turnover
Now, it is given that the sales turnover increases by 20% due to this change in price.
So, the new sales turnover is (1 + 0.2)(0.8T) = 0.96T.
Percentage increase in price
We need to find the percentage increase in the price of the detergent cake.
Let's assume the new price of the detergent cake is Q.
Since the sales turnover is directly proportional to the price of the product, we can set up the following equation:
(P/Q) = (T/0.96T)
Simplifying the equation, we get:
P/Q = 1/0.96
Cross multiplying, we get:
P = Q/0.96
Now, to find the percentage increase in price, we can use the formula:
Percentage increase = (New price - Original price) / Original price * 100
Substituting the values, we get:
Percentage increase = (Q/0.96 - P)/P * 100
Percentage increase = (Q/0.96 - Q/0.96)/Q/0.96 * 100
Percentage increase = (0.04Q)/(Q/0.96) * 100
Simplifying further, we get:
Percentage increase = 0.04/0.96 * 100
Percentage increase = 4/96 * 100
Percentage increase = 4.1667%
Since the answer options are in percentage form without decimals, we can round off the percentage increase to the nearest whole number.
Hence, the percentage increase in the price of the detergent cake is 4%.