A physical quantity C is calculated using the formula C = \frac{x \cdot y}{z}, where x, y,… — JAMB UTME

A physical quantity $C$ is calculated using the formula $C = \frac{x \cdot y}{z}$ , where $x$ , $y$ , and $z$ are positive variables. If $x$ is increased by $20\%$ , $y$ is decreased by $10\%$ , and $z$ is increased by $25\%$ , what is the net percentage change in $C$ ?

13.6% decreaseAnswer
B
15.0% decrease
C
35.0% increase
D
15.7% decrease

Answer

13.6% decrease

The new value

C'

is related to the original value

C

by the scale factor

\frac{1.20 \times 0.90}{1.25} = \frac{1.08}{1.25} = 0.864

. Subtracting 1 gives

-0.136

, which corresponds to a 13.6% decrease.

Step-by-Step Solution

Express the modified variables in terms of their original values using decimal multipliers.

x' = 1.20x

y' = 0.90y

, and

z' = 1.25z

An increase of 20% corresponds to a factor of 1.20, a decrease of 10% corresponds to 0.90, and an increase of 25% corresponds to 1.25.

Substitute the modified variables into the formula for

C

C' = \frac{(1.20x)(0.90y)}{1.25z} = \left(\frac{1.20 \times 0.90}{1.25}\right) \frac{xy}{z} = \left(\frac{1.08}{1.25}\right) C

Separate the numerical scale factor from the original expression

C = \frac{xy}{z}

Evaluate the combined scale factor as a decimal.

\frac{1.08}{1.25} = \frac{108}{125} = \frac{864}{1000} = 0.864

Multiplying the numerator and denominator by 8 simplifies the fraction to a thousandths decimal.

Calculate the net percentage change in

C

\text{Percentage Change} = (0.864 - 1) \times 100\% = -0.136 \times 100\% = -13.6\%

A factor less than 1 indicates a decrease of

(1 - 0.864) \times 100\% = 13.6\%

Key Concept

Compound Percentage Change and Variable Multipliers

Question

Answer

Step-by-Step Solution

Key Concept

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