if height of tower A is less than 42 6/7 % more than height of tower B . then height of tower B is what % of less than tower A.

Let the height of Tower B be \( B \).

Given that the height of Tower A is 42 6/7% more than the height of Tower B, we first convert 42 6/7% to an improper fraction:

\[
42 \frac{6}{7} = 42 + \frac{6}{7} = \frac{294}{7} + \frac{6}{7} = \frac{300}{7}
\]

Thus, Tower A is \(\frac{300}{7}\)% more than Tower B. To express this as a decimal, we convert the fraction to a decimal:

\[
\frac{300}{7} \approx 42.8571
\]

Therefore, Tower A is approximately 42.8571% more than Tower B.

Next, we let the height of Tower A be \( A \). Since \( A \) is 42.8571% more than \( B \), we can write:

\[
A = B + \frac{300}{7} \times B = B + 42.8571\% \times B = B \left(1 + \frac{300}{700}\right) = B \left(1 + \frac{3}{7}\right)
\]

So,

\[
A = B \left(1 + \frac{3}{7}\right) = B \left(\frac{10}{7}\right)
\]

Now, we need to find the percentage by which the height of Tower B is less than the height of Tower A. 

We know:

\[
B = A \times \left(\frac{7}{10}\right)
\]

The percentage reduction in height from Tower A to Tower B can be found by:

\[
\text{Percentage reduction} = \left(1 - \frac{B}{A}\right) \times 100\%
\]

Since:

\[
\frac{B}{A} = \frac{\frac{7}{10}A}{A} = \frac{7}{10}
\]

\[
\text{Percentage reduction} = \left(1 - \frac{7}{10}\right) \times 100\% = \left(\frac{3}{10}\right) \times 100\% = 30\%
\]

Thus, the height of Tower B is 30% less than the height of Tower A.

Would you like any further details or have any questions?

Here are 5 questions you might find interesting:
1. How do you solve equations involving percentages and ratios?
2. What is the difference between a percentage increase and a percentage decrease?
3. How can we convert between fractions, decimals, and percentages?
4. How do we solve word problems involving percentages?
5. What are some common mistakes to avoid when working with percentages?

Tip: Always convert mixed fractions to improper fractions for easier calculation, especially when dealing with percentages.

Learn how to calculate tower heights using percentages with a detailed step-by-step solution. This problem covers concepts such as percentage increase and decrease, fraction to decimal conversion, and their application in real-world scenarios. Suitable for students in Grades 7-9.

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