Common Information

Study the bar chart and answer the question based on it.

Common Information Question: 1/5

What was the percentage decline in the production of fertilizers from 1997 to 1998?

33%

20%

25%

21%

Solution:Option(C) is correct

Required percentage:

$=\dfrac{45 - 60}{ 60}\%$

$= -25\%$

There is a decline of 25% in production from 1997 to 1998

Common Information Question: 2/5

The average production of 1996 and 1997 was exactly equal to the average production of which of the following pairs of years?

2000 and 2001

1999 and 2000

1998 and 2000

1995 and 2001

Solution:Option(D) is correct

Average production (in 10000 tonnes) of 1996 and 1997:

$=\dfrac{40 + 60}{ 2}= 50$

We shall find the average production (in 10000 tonnes) for each of the given alternative pairs:

\begin{align*} \text{2000 and 2001,}\\ &=\dfrac{50 + 75}{2}\\ &= 62.5\\ \text{1999 and 2000,}\\ &=\dfrac{65 + 50}{2}\\ &= 57.5\\ \text{1998 and 2000,}\\ &=\dfrac{45 + 50}{2}\\ &= 47.5\\ \text{1995 and 1999,}\\ &=\dfrac{25 + 65}{2}\\ &= 45 \\ \text{1995 and 2001,}\\ &=\dfrac{25 + 75}{2}\\ &= 50 \end{align*}

The average production of 1996 and 1997 is equal to the average production of 1995 and 2001

Common Information Question: 3/5

What was the percentage increase in production of fertilizers in 2002 compared to that in 1995?

320%

300%

220%

200%

$=\left[\dfrac{80 - 25}{ 25} × 100\right]\%$

= 220%

Common Information Question: 4/5

In which year was the percentage increase in production as compared to the previous year the maximum?

2002

2001

1997

1996

The percentage increase in production compared to previous year for different years are:

$\begin{align*} \text{In 1996,}\\ &=\left[\dfrac{40 - 25}{25} × 100\right]\%\\ &= 60\%.\\ \text{In 1997,}\\ &=\left[\dfrac{60 - 40}{40} × 100\right]\%\\ &= 50\%. \end{align*}$

In 1998 there is a decrease in production.

$\begin{align*} \text{In 1999,}\\ & =\left[\dfrac{65 - 45}{ 45} × 100\right]\%\\ & = 44.44\% \end{align*}$

In 2000 there is a decrease in production.

$\begin{align*} \text{In 2001,}\\ & =\left[\dfrac{75 - 50}{ 50} × 100\right]\%\\ & = 50\%.\\ \text{In 2002,}\\ & =\left[\dfrac{80 - 75}{ 75} × 100\right]\%\\ & = 6.67\%. \end{align*}$

Clearly, there is maximum percentage increase in production in 1996

Edit: A typo has been corrected in the question ('precious' has been chenged to 'previous') after it was pointed out by Ameya.

Common Information Question: 5/5

In how many of the given years was the production of fertilizers more than the average production of the given years?

1

2

3

4

Average production (in 10000 tonnes) over the given years:

$=\dfrac{1}{8} × (25 + 40 + 60 + 45 + 65 + 50 + 75 + 80)$

$= 55$

The productions during the years 1997, 1999, 2001 and 2002 are more than the average production. So there are total of 4 such years.

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