Bar Charts Questions & Answers - Page 8

The percentage increase in the amount invested in raw-materials as compared to the previous year, for different years are:

For 1996 = [ (225 - 120)/120 ] % = 87.5%

For 1997 = [ (375 - 225)/225 ] % = 66.67%

For 1998, there is a decrease.

For 1999 = [ (525 - 330)/330 ] % = 59.09%

For 2000, there is a decrease.

Therefore, there is maximum percentage increase in 1996.

The percentage change in the amount invested in raw-materials and in the value of sales of finished goods for different years are:

Percentage change in Amount invested in raw-material:

For 1996 = [ (225 - 120)/120 x 100 ] % = 87.5%

For 1997 = [ (375 - 225)/225 x 100 ] % = 66.67%

For 1998 = [ (330 - 375)/375 x 100 ] % = -12%

For 1999 = [ (525 - 330)/330 x 100 ] % = 59.09%

For 2000 = [ (420 - 525)/525 x 100 ] % = -20%

Percentage change in value of sales of finished goods:

For 1996 = [ (300 - 200)/200 x 100 ] % = 50%

For 1997 = [ (500 - 300)/300 x 100 ] % = 66.7%

For 1998 = [ (400 - 500)/500 x 100 ] % = -20%

For 1999 = [ (600 - 400)/400 x 100 ] % = 50%

For 2000 = [ (460 - 600)/600 x 100 ] % = -23.33%

Thus, the percentage difference is same during the year 1997.

Required difference

= Rs. [ 1/6 x (200 + 300 + 500 + 400 + 600 +460) - 1/6 x (120 + 225 + 375 + 330 + 525 + 420) ] lakhs 

= Rs. [ ( 2460/6 ) - ( 1995/6 ) ] lakhs

= Rs. (410 - 332.5) lakhs

= Rs. 77.5 lakhs.

Required percentage = [ 600/(375 + 330 + 525) x 100 ] %

= 48.78%

≈  49%.

The differences between the amount invested in raw material and the value of sales of finished goods for various years are:

For 1995 = Rs. (200 - 120) lakhs = Rs. 80 lakhs.

For 1996 = Rs. (300 - 225) lakhs = Rs. 75 lakhs.

For 1997 = Rs. (500 - 375) lakhs = Rs. 125 lakhs.

For 1998 = Rs. (400 - 330) lakhs = Rs. 70 lakhs.

For 1999 = Rs. (600 - 525) lakhs = Rs. 75 lakhs.

For 2000 = Rs. (460 - 420) lakhs = Rs. 40 lakhs.

Clearly, maximum difference was during 1997.

Lakh tonne = 100,000

Therefore required difference = [(45 - 25) x 100,000] tons = 2,000,000 tons.

Percentage increase in the production of Company Y from 1996 to 1999

= [ (40 - 25)/25 x 100 ] % 

= [ 15/25 x 100 ] %

= 60%.

The percentages of production of Company Z to the production of Company Z for various years are:

For 1996 = ( 35/25 x 100 ) % = 140%

For 1997 = ( 40/35 x 100 ) % = 114.29%

For 1998 = ( 45/35 x 100 ) % = 128.57%

For 1999 = ( 35/35 x 100 ) % = 87.5%

For 2000 = ( 35/35 x 100 ) % = 70%

Clearly, this percentage is highest for 1996.

Average production (in lakh tons) in five years for the three companies are:

For Company X = [ 1/5 x (30 + 45 + 25 + 50 + 40) ] = 190/5 = 38

For Company Y = [ 1/5 x (25 + 35 + 35 + 40 + 50) ] = 185/5 = 37

For Company Z = [ 1/5 x (35 + 40 + 45 + 35 + 35) ] = 190/5 = 38

Therefore Average production of five years is maximum for both the Companies X and Z.

Average production of Company X in the period 1998-2000

= [ 1/3 x (25 + 50 + 40) ] = ( 115/3 ) lakh tons

Average production of Company Y in the period 1998-2000

= [ 1/3 x (35 + 40 + 50) ] = ( 125/3 ) lakh tons

Therefore Required ratio = (115/3)/(125/3)  = 115/125 = 23/25