Answer the questions on the basis of the data given in the two charts below.
Sodium carbonate, also called soda ash, is an important ingredient for glass, soap, detergents and many other products. There are two ways to produce soda ash. The first is producing soda ash from trona, which is obtained naturally; this is called natural soda ash. The second is producing soda ash from common salt through the Solvay process; soda ash made this way is called synthetic soda ash. Tata Chemicals was one of the largest producers of soda ash. The charts below show Tata Chemicals' own production of the two varieties of soda ash, and the world's total production of the two varieties.
69. Suppose the total global production increased, year on year, from 2006 to 2008 by the same amount that Tata Chemicals' synthetic production increased, year on year, over the same period. By what percentage did the total global production increase from 2007 to 2008?
Show Hint
Find how much Tata's synthetic soda ash output changed from 2007 to 2008, since the world total is defined to move by the same amount in the same year.
Cannot be calculated at all from the tables above.
Increased by 10.16%.
Increased by 9.48%.
Did not increase at all.
Show Solution
The Correct Option isD
Solution and Explanation
Step 1: Understanding the Concept:
This question links two series: Tata's synthetic soda ash output, which we can read off the chart, and the world's total output, whose year-on-year change is defined, for this question, to match Tata's synthetic change exactly.
Step 2: Key Formula or Approach:
Percentage change from 2007 to 2008 $=\dfrac{\text{change in world total}}{\text{world total in 2007}}\times100$, and by the question's rule, the change in world total equals the change in Tata's synthetic output over the same year.
Step 3: Detailed Explanation:
Tata's synthetic soda ash output reads $0.7$ MT in 2006, $2.2$ MT in 2007 and $2.2$ MT in 2008. So going from 2007 to 2008, Tata's synthetic output does not change at all: $2.2-2.2=0$.
By the question's condition, the world's total production also changes by this same $0$ MT from 2007 to 2008. It does not matter that we do not know the exact world total for those two years, which is why option A, "cannot be calculated", looks tempting; the percentage change only needs the SIZE of the change, and a $0$ change gives a $0\%$ change regardless of the base value.
Step 4: Final Answer:
The world's total production did not increase at all from 2007 to 2008, so the answer is option D.
