A store increased the original price of a shirt by a certain percent and then decreased the new price by the same percent. Given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?
Answers
A store increased the original price of a shirt by a certain percent and then decreased the new price by the same percent. Given that the resulting price was 84% of the original price, the price was increased and decreased by 40%
Let the original price of the shirt be Rs 100 and we are increasing the price by t%.
So, after the initial t% increase, new price of shirt = 100 + (t/100 * 100) = Rs 100+t
Next, we lower the price by t%.
New price of shirt = (100+t) - (t/100)[100+t] = (100+t)[1-(t/100]
= [(100+t)/100][100-t) = 10000 - t^2. ...(1)
As mentioned in the question, the final price of the shirt is 84% of the original price (which was Rs 100), so final price = 84% of Rs 100 = Rs 84.
So (1) is equal to 84.
∴ 10000 - t^2 = 84.
⇒ t^2 = 1600
⇒ t = ±40
⇒ t = 40 [As percentage cannot be negative]
So, by 40%, the price was increased and decreased.
The price was increased and decreased by 40%
Step-by-step explanation:
Given:
A store increased the original price of a shirt by a certain percent and then decreased the new price by the same percent.
Given that the resulting price was 84% of the original price.
By what percent was the price increased and decreased?
Solution:
Let the original price of the shirt be 100 rupees.
84% of the original price = 84 rupees.
Consider, the percent increase as 40%
40% of 100 rupees is 40, 100+ 40 = 140
40% of 140 rupees = 56
140 – 56 = 84 which 84 % of the original price
The price was increased and decreased by 40%
To know more:
A number is first increased by 20% and then decreased by 15%. find the net increase or decrease percent
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