The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be reduction in the usage of raw materials so as to keep the cost same?
Initial cost:
$$R+L$$
$$=R+\frac{1}{4}R$$
Final Cost
$$\frac{115}{100}R+\frac{3}{10}\frac{115}{100}R$$
ATQ
$$\frac{5}{4} R*C=\frac{115}{100}\frac{13}{10}R*C'$$
$$C'=\frac{250}{299}C$$
Therefore,
Required percentage=
$$=\frac{49}{299}*100$$
,which comes close to 16.38 percent.
However the answer given is 17%. Have I done anything wrong?