At the beginning of 2023, a manufacturing plant had an initial annual production capacity … — GMAT

At the beginning of 2023, a manufacturing plant had an initial annual production capacity of $C$ units. Over the next three years, its annual production capacity experienced the following changes: it increased by $10\%$ in 2023, decreased by $20\%$ in 2024, and increased by $25\%$ in 2025. If the plant's production capacity at the end of 2025 was $22,000$ units, what was the initial production capacity $C$ , in units, at the beginning of 2023?

Cevap: 20000 units

Cevap

The initial production capacity at the beginning of 2023 was 20,000 units.

Each annual percentage change applies to the value at the end of the previous period. Representing the changes as multipliers gives

1.10

0.80

, and

1.25

. Multiplying these together gives a net change factor of

1.10 \times 0.80 \times 1.25 = 1.10

. Setting

1.10 C = 22,000

and solving for

C

yields

C = 20,000

Adım Adım Çözüm

Convert each percentage change into a decimal multiplier

Increase of

10\% \rightarrow 1.10

; decrease of

20\% \rightarrow 0.80

; increase of

25\% \rightarrow 1.25

Successive percentage changes compound sequentially by multiplying their respective growth or decay factors.

Compute the overall compound multiplier factor

Overall multiplier =

1.10 \times 0.80 \times 1.25 = 1.10 \times (0.80 \times 1.25) = 1.10 \times 1 = 1.10

Multiplying

0.80 \times 1.25

yields

1

, simplifying the combined factor to

1.10

times the original capacity.

Solve for the initial capacity

C

1.10 \times C = 22,000 \implies C = \frac{22,000}{1.10} = 20,000

Dividing the final capacity by the combined multiplier yields the initial capacity.

Anahtar Kavram

Successive Percent Change

Soru

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