Subjects algebra

Salary Increase

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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%