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The respective ratio of two number is 16 : 21. If the first number is increased by 30% and the second number is decreased by 20%, what will be the respective ratio of the first and the second number?
  • a)
    32 : 21
  • b)
    26 : 21
  • c)
    25 : 21
  • d)
    20 : 21
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The respective ratio of two number is 16 : 21. If the first number is ...
Let the first number be 16x
and second number be 21x


∴ Option (b) is correct.
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The respective ratio of two number is 16 : 21. If the first number is ...
Given:
The respective ratio of two numbers is 16 : 21.

To find:
The respective ratio of the first and the second number after the increase and decrease in percentages.

Solution:
Let the first number be 16x and the second number be 21x, where x is a constant.

Step 1: Increase in the first number by 30%
The first number is increased by 30%, which means it becomes (100% + 30%) = 130% of its original value.
Therefore, the new value of the first number is 16x + (30/100) * 16x = 16x + (8/10) * 16x = 16x + 12.8x = 28.8x.

Step 2: Decrease in the second number by 20%
The second number is decreased by 20%, which means it becomes (100% - 20%) = 80% of its original value.
Therefore, the new value of the second number is 21x - (20/100) * 21x = 21x - (4.2x) = 16.8x.

Step 3: Finding the respective ratio of the first and the second number after the increase and decrease
The respective ratio of the first and second number after the increase and decrease can be found by dividing the new values obtained in Step 1 and Step 2.
Therefore, the ratio is (28.8x)/(16.8x) = 288/168 = 24/14 = 12/7.

Step 4: Simplify the ratio
The ratio 12/7 can be simplified further.
Divide both the numerator and denominator by their greatest common divisor, which is 2.
The simplified ratio is (12/2) / (7/2) = 6/3 = 2/1.

Therefore, the respective ratio of the first and the second number after the increase and decrease is 2 : 1, which is equivalent to 26 : 21.

Hence, the correct answer is option 'B' (26 : 21).
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The respective ratio of two number is 16 : 21. If the first number is increased by 30% and the second number is decreased by 20%, what will be the respective ratio of the first and the second number?a)32 : 21b)26 : 21c)25 : 21d)20 : 21Correct answer is option 'B'. Can you explain this answer?
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