A person’s salary decreases by 10% every year, while the bonus increases by…
2023
A person’s salary decreases by 10% every year, while the bonus increases by 24% every year. If the salary and bonus in March 2020 were ₹8,000 and ₹2,500 respectively, find the difference between the total earnings in March 2020 and March 2022.
Answer: D. ₹ 176, decrease — ConceptFor an amount that changes by the same rate each year, the value after n years is initial value × (1 ± rate)n. When earnings have separate components,…
- A.
₹ 165, increase
- B.
₹ 176, increase
- C.
₹ 180, decrease
- D.
₹ 176, decrease
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept
For an amount that changes by the same rate each year, the value after n years is initial value × (1 ± rate)n. When earnings have separate components, update each component independently before adding them.
Application
Let S0 = ₹8,000 and B0 = ₹2,500 for March 2020. Therefore, total earnings in March 2020 are E0 = 8,000 + 2,500 = ₹10,500.
The salary retention factor is 1 − 0.10 = 0.90. After two years, S2 = 8,000 × 0.90 × 0.90 = ₹6,480.
The bonus growth factor is 1 + 0.24 = 1.24. After two years, B2 = 2,500 × 1.24 × 1.24 = ₹3,844.
Thus, total earnings in March 2022 are E2 = 6,480 + 3,844 = ₹10,324.
The difference is E0 − E2 = 10,500 − 10,324 = ₹176, so total earnings decreased by ₹176.
Cross-check
A component-wise check gives a salary decrease of ₹1,520 and a bonus increase of ₹1,344. Their net effect is −₹1,520 + ₹1,344 = −₹176, confirming a decrease of ₹176.
Result
Therefore, the total earnings decreased by ₹176.