Question

The profits of Biscuits India Ltd rose by 32% in the year 2006-07 compared to the year 2005-06. By what percentage did Biscuits India's Sales increase in 2006-07 compared to the previous year? (Assume: Profit = Sales - Expenses.) Decide whether the information given in the two statements below is enough to answer the question.

Statement (1): Expenses in 2006-07 were Rs 1,400 crores, compared to Rs 1,220 crores in 2005-06.
Statement (2): Sales in 2006-07 were Rs 4,300 crores.

• A. Any one of the two statements (1) or (2) taken alone is enough to answer the question.
• B. Each of the statements (1) or (2) taken alone is enough to answer the question.
• C. Both statements together are enough to answer the question, but neither one alone is enough.
• D. Both statements together are not enough to answer the question.

Hint:

Set up Sales = Profit + Expenses for both years using \(P'=1.32P\), and see how many unknowns remain after each statement.

Answer 1

The Correct Option is C

Step 1: Understanding the Question.
Let \(S\) be Sales and \(P\) be Profit for 2005-06, and \(S'\) and \(P'\) be Sales and Profit for 2006-07. We are told \(P' = 1.32P\), since profit rose by 32%. We need the percentage rise in Sales, that is \(\frac{S'-S}{S}\times 100\). Since Profit = Sales minus Expenses, we can write \(S = P + 1220\) and \(S' = P' + 1400\), using the expense figures from Statement (1).

Step 2: Check Statement (1) alone.
Statement (1) gives both years' expenses, so \(S = P+1220\) and \(S'=1.32P+1400\). This is two equations in three unknowns (\(S\), \(S'\), \(P\)), so we cannot pin down a single value for the percentage rise. Statement (1) alone is not enough.

Step 3: Check Statement (2) alone.
Statement (2) only tells us \(S' = 4300\). We still do not know \(P\), \(P'\), or \(S\), so the percentage rise cannot be found. Statement (2) alone is not enough.

Step 4: Combine both statements.
Using \(S' = P'+1400\) and \(S'=4300\) from Statement (2), we get \(P' = 4300-1400=2900\). Since \(P'=1.32P\), \(P = \frac{2900}{1.32} \approx 2196.97\). Then from Statement (1), \(S = P+1220 \approx 2196.97+1220=3416.97\). Now both \(S\) and \(S'\) are known numbers, so the percentage rise is
\[ \frac{S'-S}{S}\times 100 = \frac{4300-3416.97}{3416.97}\times 100 \approx 25.84\% \]

Step 5: Final Answer.
Only when both statements are used together can the percentage rise in sales be pinned down to one number, so neither statement alone is enough but both together are. \[ \boxed{\text{Both statements together are sufficient, neither alone is sufficient}} \]