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If a quantity A is successively increased by 20% for two times and another quantity B is successively increased by 10% for three times, then quantity A becomes 80% of quantity B. What percentage is the original value of quantity A as compared to the original value of quantity B?
  • a)
    50%
  • b)
    58%
  • c)
    63%
  • d)
    74%
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If a quantity A is successively increased by 20% for two times and ano...
Option (4) is correct.
Let quantity A be x.
Two successive increase of 20% on x gives us 1.44x.
Let quantity B be y.
Three successive increase of 10% on y gives 1.331y.
Now, 80% of 1.331y = 1.44x
x = 0.739y
That is, x is 74% of y.
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Community Answer
If a quantity A is successively increased by 20% for two times and ano...
To solve this problem, we need to determine the original values of quantities A and B and then compare them.

Let's assume the original value of quantity A is x, and the original value of quantity B is y.

Step 1: Successive increases of 20% for two times on quantity A
After the first increase of 20%, quantity A becomes x + 0.2x = 1.2x
After the second increase of 20%, quantity A becomes 1.2x + 0.2(1.2x) = 1.2x + 0.24x = 1.44x

Step 2: Successive increases of 10% for three times on quantity B
After the first increase of 10%, quantity B becomes y + 0.1y = 1.1y
After the second increase of 10%, quantity B becomes 1.1y + 0.1(1.1y) = 1.1y + 0.11y = 1.21y
After the third increase of 10%, quantity B becomes 1.21y + 0.1(1.21y) = 1.21y + 0.121y = 1.331y

Step 3: Compare the values of quantities A and B
According to the given information, quantity A becomes 80% of quantity B. Mathematically, this can be expressed as:
1.44x = 0.8 * 1.331y

Simplifying the equation, we get:
1.44x = 1.065y

Step 4: Determine the ratio of the original values of A and B
To find the ratio of the original values, we divide both sides of the equation by 1.44y:
x/y = 1.065/1.44

To convert this ratio into a percentage, we multiply it by 100:
(x/y) * 100 = (1.065/1.44) * 100 ≈ 74%

Therefore, the original value of quantity A is approximately 74% of the original value of quantity B. Hence, the correct answer is option D) 74%.
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