Question

A physical quantity x is being calculated by measuring y and z and using the formula x = y × z. In a particular set of values, the value of y is measured with an error of +10%, whereas the value of z is measured with an error of -10%. For this particular set of values, the error in the calculation of x will be

• A. 0%
• B. 20%
• C. -1%
• D. 10%

Answer 1

Answer: (C)

-1%

Answer 2

Explanation: We have

$$x = y \times z.$$

If $y$ is measured with +10% error and $z$ with -10% error, then

$$y' = 1.1y \quad \text{and} \quad z' = 0.9z.$$

Therefore,

$$x' = y' \times z' = 1.1y \times 0.9z = 0.99yz = 0.99x.$$

The calculated value of $x$ is 0.99 times the actual value, which means the error is

$$\text{Error} = (0.99 - 1) \times 100\% = -1\%.$$

Answer: Option (C) $-1\%$