The price of groundnuts increased by X % per week over two successive weeks…
2024
The price of groundnuts increased by X % per week over two successive weeks .If at the beginning 2 kgs were available for rupees 80 and after 2 weeks they were available for rupees 105.80, what is the value of x?
- A.
10%
- B.
12%
- C.
15%
- D.
20%
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Correct answer: C
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Let the weekly percentage increase be x%. The weekly multiplier is (1 + x/100). After two weeks the multiplier is (1 + x/100)^2.
Initial price for 2 kg = 80. Final price after 2 weeks = 105.80. So:
80 × (1 + x/100)^2 = 105.80
Divide both sides by 80: (1 + x/100)^2 = 105.80 / 80 = 1.3225
Take square root: 1 + x/100 = √1.3225 = 1.15
So x/100 = 0.15 ⇒ x = 15
Verification: 80 × (1.15)^2 = 80 × 1.3225 = 105.80, which matches the given final price.
Answer: 15%