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Weights of two friends A and B are in the ratio of 1:2. A’s weight increases by 20% and the total weight of A and B together becomes 60 kg, with an increase of 30%. By what percent the weight of B increase?
- a)30%
- b)35%
- c)40%
- d)45%
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Weights of two friends A and B are in the ratio of 1:2. A’s weig...
Understanding the Problem
To solve the problem, we need to establish the weights of A and B based on the given ratio and changes due to weight increase.
Initial Weights of A and B
- Let A's weight be x kg.
- Then, B's weight = 2x kg (since the ratio of A to B is 1:2).
Weight Increase of A
- A's weight increases by 20%.
- New weight of A = x + 0.2x = 1.2x kg.
Total Weight After Increases
- The total weight of A and B becomes 60 kg after increases.
- Therefore, the equation is:
1.2x + 2x = 60.
Simplifying the Equation
- Combining the weights gives us: 3.2x = 60.
- Solving for x:
x = 60 / 3.2 = 18.75 kg.
Calculating A and B's Weights
- A's initial weight = 18.75 kg.
- B's initial weight = 2 * 18.75 = 37.5 kg.
Calculating New Weight of B
- The total weight of A and B increased by 30%.
- Total initial weight = 18.75 + 37.5 = 56.25 kg.
- New total weight = 56.25 * 1.3 = 73.125 kg.
Finding B's New Weight
- A's new weight = 1.2 * 18.75 = 22.5 kg.
- Therefore, B's new weight = 73.125 kg - 22.5 kg = 50.625 kg.
Percentage Increase in B's Weight
- B's weight increased from 37.5 kg to 50.625 kg.
- Increase = 50.625 - 37.5 = 13.125 kg.
- Percentage increase = (13.125 / 37.5) * 100 = 35%.
Conclusion
Thus, the weight of B increases by 35%, which is option 'B'.
To solve the problem, we need to establish the weights of A and B based on the given ratio and changes due to weight increase.
Initial Weights of A and B
- Let A's weight be x kg.
- Then, B's weight = 2x kg (since the ratio of A to B is 1:2).
Weight Increase of A
- A's weight increases by 20%.
- New weight of A = x + 0.2x = 1.2x kg.
Total Weight After Increases
- The total weight of A and B becomes 60 kg after increases.
- Therefore, the equation is:
1.2x + 2x = 60.
Simplifying the Equation
- Combining the weights gives us: 3.2x = 60.
- Solving for x:
x = 60 / 3.2 = 18.75 kg.
Calculating A and B's Weights
- A's initial weight = 18.75 kg.
- B's initial weight = 2 * 18.75 = 37.5 kg.
Calculating New Weight of B
- The total weight of A and B increased by 30%.
- Total initial weight = 18.75 + 37.5 = 56.25 kg.
- New total weight = 56.25 * 1.3 = 73.125 kg.
Finding B's New Weight
- A's new weight = 1.2 * 18.75 = 22.5 kg.
- Therefore, B's new weight = 73.125 kg - 22.5 kg = 50.625 kg.
Percentage Increase in B's Weight
- B's weight increased from 37.5 kg to 50.625 kg.
- Increase = 50.625 - 37.5 = 13.125 kg.
- Percentage increase = (13.125 / 37.5) * 100 = 35%.
Conclusion
Thus, the weight of B increases by 35%, which is option 'B'.
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Community Answer
Weights of two friends A and B are in the ratio of 1:2. A’s weig...
weight of A is x and weight of B is 2x
given that 60 kg weight is the 30% percent increase of the original weight, so
(130/100)*W = 60, W = 600/13 kg (W = original weight)
X + 2x = 600/13, x = 200/13
So weight of A = 200/13 and of B = 400/13
(120/100)*(200/13) + [(100 + a)/100]*(400/13) = 60
Solve for a. We will get a = 35%
given that 60 kg weight is the 30% percent increase of the original weight, so
(130/100)*W = 60, W = 600/13 kg (W = original weight)
X + 2x = 600/13, x = 200/13
So weight of A = 200/13 and of B = 400/13
(120/100)*(200/13) + [(100 + a)/100]*(400/13) = 60
Solve for a. We will get a = 35%
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Weights of two friends A and B are in the ratio of 1:2. A’s weight increases by 20% and the total weight of A and B together becomes 60 kg, with an increase of 30%. By what percent the weight of B increase?a)30%b)35%c)40%d)45%Correct answer is option 'B'. Can you explain this answer?
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