Salary Increase
1. State the problem: The salaries of Rafayet, Nihan, and Shafiul were in the ratio $6:5:7$ in 2010 and changed to $3:4:3$ in 2015. Rafayet's salary increased by 25% from 2010 to 2015. We need to find the percentage increase in Shafiul's salary during this period.
2. Let the salaries in 2010 be $6x$, $5x$, and $7x$ for Rafayet, Nihan, and Shafiul respectively.
3. From the ratios in 2015, let the salaries be $3y$, $4y$, and $3y$ respectively.
4. Since Rafayet's salary increased by 25%, we have:
$$3y = 6x \times 1.25 = 7.5x$$
5. Solving for $y$, we get:
$$y = \frac{7.5x}{3} = 2.5x$$
6. Therefore, Shafiul's salary in 2015 is:
$$3y = 3 \times 2.5x = 7.5x$$
7. Shafiul's salary in 2010 was $7x$, so the increase is:
$$7.5x - 7x = 0.5x$$
8. The percentage increase in Shafiul's salary is:
$$\frac{0.5x}{7x} \times 100 = \frac{0.5}{7} \times 100 \approx 7.14\%$$
9. The closest percentage increase option is $7\%$.
Final answer: 7%