Question

If $a,b,c$ are the percentage errors in the measurement of $A,B,C$ then percentage error in $ABC$ would be

• A. $abc$
• B. $a+b+c$
• C. $ab+bc+ca$
• D. $a-b-c$

Answer 1

The correct option is B $a+b+c$

Given,

$\frac{dA}{A}\times 100=a$

$\frac{dB}{B}\times 100=b$

$\frac{dC}{C}\times 100=c$

Let,

$Y=ABC$

taking logarithm,

$log\left(y\right)=log\left(A\right)+log\left(B\right)+lig\left(C\right)$

$\frac{dY}{Y}=\frac{dA}{A}+\frac{dB}{B}+\frac{dC}{C}$

Hence Option $\text{B}$ is the correct answer