Question 15 Marks
Answer
View full question & answer→(i) Percentage rise/fall in the production of company Y from 1996 to 1999
$
=\left[\frac{(40-25)}{25} \times 100\right] \%
$
$
\begin{array}{l}
=\left[\frac{15}{25} \times 100\right] \% \\
=60 \%
\end{array}
$
Therefore, percentage rise in the production of company $Y$ from 1996 to 1999 was $60 \%$.
(ii) Average production of company $X$ in the period 1998-2000
$
\begin{array}{l}
=\left[\frac{1}{3} \times(25+50+40)\right] \\
=\left(\frac{115}{3}\right) \text { lakh tonnes }
\end{array}
$
Average production of company $Y$ in the period 1998-2000
$
=\left[\frac{1}{3} \times(35+40+50)\right]
$
$\begin{aligned} & =\left(\frac{125}{3}\right) \text { lakh tonnes } \\ \therefore \quad \text { Required Ratio } & =\frac{\left(\frac{115}{3}\right)}{\left(\frac{125}{3}\right)}=\frac{115}{125} \\ & =\frac{23}{25} \text { or } 23: 25\end{aligned}$
(iii) Average production (in lakh tonnes) in five years for the three companies are :
For company
$
\begin{aligned}
y & =\left[\frac{1}{5} \times(30+45+25+50+40)\right] \\
& =\frac{190}{5}=38
\end{aligned}
$
$\begin{aligned} \text { For company } Y & =\left[\frac{1}{5} \times(25+35+35+40+50)\right] \\ & =\frac{185}{5}=37 \\ \text { For company } Z & =\left[\frac{1}{5} \times(35+40+45+35+35)\right] \\ & =\frac{190}{5}=38\end{aligned}$
$
=\left[\frac{(40-25)}{25} \times 100\right] \%
$
$
\begin{array}{l}
=\left[\frac{15}{25} \times 100\right] \% \\
=60 \%
\end{array}
$
Therefore, percentage rise in the production of company $Y$ from 1996 to 1999 was $60 \%$.
(ii) Average production of company $X$ in the period 1998-2000
$
\begin{array}{l}
=\left[\frac{1}{3} \times(25+50+40)\right] \\
=\left(\frac{115}{3}\right) \text { lakh tonnes }
\end{array}
$
Average production of company $Y$ in the period 1998-2000
$
=\left[\frac{1}{3} \times(35+40+50)\right]
$
$\begin{aligned} & =\left(\frac{125}{3}\right) \text { lakh tonnes } \\ \therefore \quad \text { Required Ratio } & =\frac{\left(\frac{115}{3}\right)}{\left(\frac{125}{3}\right)}=\frac{115}{125} \\ & =\frac{23}{25} \text { or } 23: 25\end{aligned}$
(iii) Average production (in lakh tonnes) in five years for the three companies are :
For company
$
\begin{aligned}
y & =\left[\frac{1}{5} \times(30+45+25+50+40)\right] \\
& =\frac{190}{5}=38
\end{aligned}
$
$\begin{aligned} \text { For company } Y & =\left[\frac{1}{5} \times(25+35+35+40+50)\right] \\ & =\frac{185}{5}=37 \\ \text { For company } Z & =\left[\frac{1}{5} \times(35+40+45+35+35)\right] \\ & =\frac{190}{5}=38\end{aligned}$
