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: Set up the two years side by side.
Call last year's sales and profit $s$ and $p$, and this year's sales and profit $s_1$ and $p_1$. We know $p_1 = 1.32p$ (32% profit growth) and Profit = Sales minus Expenses. We want $\frac{s_1-s}{s}\times 100$.

Step 2: Try Statement (1) by itself.
Statement (1) hands us the expense numbers only: Rs 1,220 crore last year and Rs 1,400 crore this year. That gives $s = p + 1220$ and $s_1 = 1.32p+1400$, which is 2 equations but 3 unknowns ($s$, $s_1$, $p$). No unique sales growth number comes out. Not sufficient alone.

Step 3: Try Statement (2) by itself.
Statement (2) hands us this year's sales, $s_1=4300$, and nothing about expenses or profit values. There is no way to find $s$ from this alone. Not sufficient alone.

Step 4: Merge the two statements.
Plug $s_1=4300$ into $s_1 = 1.32p+1400$: $4300 = 1.32p+1400$, so $1.32p = 2900$ and $p = 2900/1.32$. Rounding, $p \approx 2196.97$. Now use Statement (1)'s expense figure for last year: $s = p+1220 \approx 3416.97$.

Step 5: Compute the growth rate.
\[ \text{Growth} = \frac{4300-3416.97}{3416.97}\times 100 \approx 25.84\% \]
A single definite number comes out only once both statements are combined, so both are required together and neither is enough alone.
\[ \boxed{\text{Both statements together are sufficient, neither alone is}} \]