At the beginning of 2021, a biotechnology firm allocated a fixed annual budget to its prin… — GMAT

At the beginning of 2021, a biotechnology firm allocated a fixed annual budget to its principal research laboratory. In 2022, the laboratory's budget was increased by $20\%$ relative to its 2021 budget. In 2023, the budget was reduced by $15\%$ from its 2022 level. In 2024, the budget was increased by $25\%$ over its 2023 level. If the budget in 2024 exceeded the budget in 2021 by $\$55,000$ , what was the laboratory's budget in 2021, in dollars?

Answer: 200000 dollars

Answer

200,000 dollars

The initial 2021 budget

B

undergoes successive percentage changes over three years. A

20\%

increase in 2022 results in

1.20B

. A

15\%

decrease in 2023 yields

1.20B \times 0.85 = 1.02B

. A

25\%

increase in 2024 yields

1.02B \times 1.25 = 1.275B

. The net increase over the initial budget is

1.275B - B = 0.275B

. Setting

0.275B = 55,000

gives

B = \frac{55,000}{0.275} = 200,000

dollars.

Step-by-Step Solution

Represent the annual budgets sequentially in terms of the initial 2021 budget

B

2022 budget =

1.20B

, 2023 budget =

1.20B \times 0.85 = 1.02B

, 2024 budget =

1.02B \times 1.25 = 1.275B

Calculate successive percentage changes sequentially by multiplying the respective multipliers for each period

Calculate the net change in budget from 2021 to 2024

1.275B - B = 0.275B

Determine how much the final year's budget exceeds the initial base budget

Set up and solve the linear equation for

B

0.275B = 55,000 \implies B = \frac{55,000}{0.275} = 200,000

Equate the net algebraic difference to the given dollar amount to solve for the initial 2021 budget

Key Concept

Successive Percent Change and Base Value Tracking

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