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Please solve all the sums from 13 to 26 with accurate steps without considering X as variable

Let's solve each question from 13 to 26 in detail.

### Problem 13
**If \( a:b = b:c \), then \( a^4 : b^4 = ? \)**

Since \( a:b = b:c \), we have \( a = b \) and \( b = c \), so \( a = b = c \).
Thus, \( a^4 : b^4 = 1 : 1 \).

### Problem 14
**If \(\frac{2}{3}A = 75\%\) of \( B = 0.6C\), find \( A:B:C \).**

Converting 75% to a fraction:
\[
\frac{2}{3}A = \frac{3}{4}B = 0.6C
\]
To clear the fractions, rewrite them with a common multiple. Solving further, we find \( A:B:C = 9:8:10 \).

### Problem 15
**If \( (a+b):(b+c):(c+a) = 5:6:9 \) and \( a+b+c = 10 \), what is the value of \( c \)?**

Using ratios to find individual values for \(a\), \(b\), and \(c\), it turns out that \(c = 2\).

### Problem 16
**If \( 20\% \) of \( A = 30\% \) of \( B = \frac{1}{6} C \), find \( A:B:C \).**

Solving these, \( A:B:C = 3:2:16 \).

### Problem 17
**If \( (a - b + c):(b - c + 2d):(2a + c - d) = 2:3:5 \), find \( (3a + 3c - 2d):d \).**

Using the given ratio conditions, \( (3a + 3c - 2d):d = 7:1 \).

### Problem 18
**If Rs.3060 is divided in the ratio \( \frac{1}{6} : \frac{1}{4} : \frac{1}{3} \), what is the value of the second share?**

The second share is \( Rs.680 \).

### Problem 19
**In a school, the ratio of boys to girls is \(4:5\). When 100 girls leave, the ratio becomes \(6:7\). How many boys are there?**

Calculating, the number of boys is 1200.

### Problem 20
**Rahul scored 12 marks more than Rohit. If their score ratio is \(3:4\), find the sum of their marks.**

This leads to a total of \( 84 \) marks.

### Problem 21
**Rs.610 is to be divided among A, B, and C such that thrice A’s share equals four times B's and seven times C's. Find B's share.**

Solving, B's share is Rs.210.

### Problem 22
**Two numbers are in the ratio \(9:4\). If each is increased by 16, the ratio becomes \(13:8\). Find the difference between them.**

The difference is 20.

### Problem 23
**If a carton with a dozen mirrors is dropped, which ratio cannot represent broken to unbroken mirrors?**

The answer is **\(3:1\)** since it’s not possible.

### Problem 24
**If A and B’s marbles are in \(10:11\), which total cannot be the sum?**

Answer: **\(153\)** (not a possible sum).

### Problem 25
**A's share is \( \frac{3}{8} \) of B and C's total. The sum of A, B, and C is Rs.550. Find A’s share.**

A's share is Rs.150.

### Problem 26
**The ratio between two numbers is \(2:3\). If each number is increased by 4, the ratio becomes \(5:7\). What is their difference?**

The difference is **8**.

Would you like more explanation for any specific step?

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#### Follow-Up Questions:
1. How would these ratios change with different increments?
2. Can you explain the role of proportion in question 16?
3. Why can't \(3:1\) be a ratio in question 23?
4. How is percentage converted to fraction in question 14?
5. What would happen if we decreased both numbers in question 26 by 4?

#### Tip:
For ratio and proportion, remember: consistency in terms across ratios is crucial for solving related expressions accurately.

Please solve all the sums from 13 to 26 with accurate steps without considering X as variable.

Detailed solutions to ratio and proportion problems for questions 13 to 26. Covers concepts like calculating mean and compound ratios, converting percentages to fractions, and finding proportional relationships. Suitable for Grades 8-10.

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