The weights of two friends A and B are in the ratio 7 : 8. If the weight of A increases by 10 percent and the total combined weight of A and B increases by 20 percent, what is the percentage increase in the weight of B?

Introduction / Context:
This problem links ratio and percentage change. It gives the initial ratio of the weights of two people, then describes different percentage increases for their weights such that the total weight rises by a known percentage. You have to determine the unknown percentage change for one person, which requires setting up and solving an equation.

Given Data / Assumptions:

• Initial weight ratio A : B = 7 : 8.
• Let initial weights be 7x for A and 8x for B.
• Weight of A increases by 10 percent.
• Combined weight of A and B increases by 20 percent overall.
• We need the percentage increase in the weight of B.

Concept / Approach:
Use variables to represent the initial weights according to the ratio. Apply the 10 percent increase for A and an unknown percentage p for B. Then equate the new total weight to 120 percent (1.2 times) of the original total weight. Solving the resulting equation in p will give the required percentage increase for B.

Step-by-Step Solution:
Step 1: Let initial weights be A = 7x and B = 8x. Step 2: Initial total weight = 7x + 8x = 15x. Step 3: After 10 percent increase, A becomes 7x * 1.10 = 7.7x. Step 4: Let B increase by p percent, so new B weight = 8x * (1 + p). Step 5: New total weight must be 120 percent of original total, so new total = 1.20 * 15x = 18x. Step 6: Form the equation: 7.7x + 8x * (1 + p) = 18x. Step 7: Simplify: 7.7x + 8x + 8x * p = 18x ⇒ 15.7x + 8x * p = 18x. Step 8: Subtract 15.7x: 8x * p = 2.3x ⇒ p = 2.3 / 8 = 0.2875. Step 9: Convert to percentage: p = 0.2875 * 100 = 28.75 percent.

Verification / Alternative check:
We can plug back the percentage to verify. New B weight = 8x * 1.2875 = 10.3x. New total = 7.7x + 10.3x = 18x, which equals 120 percent of the original 15x. Hence the calculation is consistent.

Why Other Options Are Wrong:

• 11.55, 32.85, and 24.25 do not satisfy the equation when substituted as percentage increases for B and give incorrect total weights.

Common Pitfalls:
Many learners forget to apply the total increase to the combined weight, or they incorrectly treat the ratio as fixed after the percentage changes. It is important to handle each percentage change separately and then apply the total change condition systematically through algebra.

Final Answer:
The weight of B increases by 28.75 percent.