Question

Tata Chemicals' own natural and synthetic soda ash output was:

Year	Natural Soda Ash (MT)	Synthetic Soda Ash (MT)
2005	0	0.7
2007	0.4	2.2
2008	3.2	2.2

Suppose total global production of soda ash in 2008 was 40 MT, and Tata Chemicals was the second highest producer of soda ash globally, right after another company called Solvay. FMC Wyoming was the third highest producer. The two Indian giants, Tata Chemicals and Nirma, had a combined soda ash production capacity of 8.8 MT.

Which of the following statements are right?
1. Solvay's market share was more than 20.66%
2. Solvay's market share was more than 13.5%
3. FMC's share was less than 10.33%
4. FMC's share was less than 13.5%
5. Nirma, which was the sixth largest producer, had a share of less than 8.5%
Choose the right option.

• A. 1 and 3
• B. 1 and 5
• C. 2 and 4
• D. 1, 3 and 5

Hint:

Work out Tata's own 2008 share first (5.4 MT of 40 MT, which is 13.5 percent), then use Solvay greater than Tata greater than FMC to bound the other two shares, and treat the Tata plus Nirma capacity figure as a ceiling, not an exact output number.

Answer 1

The Correct Option is C

The key move here is to pin down one exact number, Tata's own 2008 share, and then use the ranking and the capacity figure to bound everyone else against it, rather than trying to compute exact shares for companies whose output is never actually given.

1. Tata's own share: Tata's 2008 output is 3.2 MT natural plus 2.2 MT synthetic, or 5.4 MT. Out of a 40 MT world total, that is $5.4/40 = 13.5$ percent exactly.
2. Statements 1 and 2 (Solvay): Solvay outranks Tata, so Solvay's share exceeds 13.5 percent. That is enough to call statement 2 true. It is not enough to call statement 1 true, since crossing 13.5 percent does not mean crossing the much higher bar of 20.66 percent.
3. Statements 3 and 4 (FMC): FMC ranks below Tata, so FMC's share is under 13.5 percent, confirming statement 4. But being under 13.5 percent does not mean being under the stricter 10.33 percent in statement 3, so statement 3 stays unconfirmed.
4. Statement 5 (Nirma): the 8.8 MT figure is a combined production capacity for Tata and Nirma, not their combined actual output. Subtracting Tata's actual 5.4 MT leaves at most 3.4 MT of capacity for Nirma, which is at most 8.5 percent of 40 MT. Since this is a ceiling exactly equal to 8.5 percent rather than a number strictly below it, the claim of less than 8.5 percent cannot be treated as proven.

Only the two claims tied directly to Tata's exact 13.5 percent benchmark, statements 2 and 4, survive scrutiny.

Let's summarize:

• Tata's 2008 share works out to exactly 13.5 percent of the 40 MT total.
• Solvay must beat 13.5 percent and FMC must fall short of it, but neither is pinned to the stricter 20.66 percent or 10.33 percent bars.
• Nirma's capacity only bounds its share at 8.5 percent, it does not prove the share is strictly below that.

So the right combination is statements 2 and 4, option C.