Question

Each of the following questions is followed by two statements, I and II. Decide whether the data given in the statements is sufficient to answer the question.

For each rupee in monthly advertising expenditure, KUMAR & Co. experiences a Rs. 6 increase in sales. How much does KUMAR & Co. have to spend on advertising to attain Rs. 1,000,000 in sales revenue for the month?

I. Without advertising, KUMAR & Co. earns Rs. 200,000 sales revenue per month.
II. When KUMAR & Co. spends Rs. 15,000 on advertising, it earns Rs. 290,000 as sales revenue.

• A. If Statement I alone is sufficient to answer the question.
• B. If Statement II alone is sufficient to answer the question.
• C. If Statement I and Statement II together are sufficient, but neither statement alone is sufficient to answer the question.
• D. If either Statement I alone or Statement II alone is sufficient to answer the question.

Hint:

The slope of the sales-advertising line is already given in the question; each statement supplies just enough extra data to fix the line completely.

Answer 1

The Correct Option is D

Step 1: Write the sales model using the fact already given.
The question tells us that every extra rupee spent on advertising raises sales by Rs. 6. If \(A\) is the advertising spend and \(S_0\) is the sales revenue with zero advertising, then
\[ S = S_0 + 6A \]
We need \(A\) such that \(S = 1{,}000{,}000\), so we only need to know \(S_0\).

Step 2: Test Statement I alone.
Statement I says \(S_0 = 200{,}000\). Put this in the model:
\[ 1{,}000{,}000 = 200{,}000 + 6A \implies A = \frac{800{,}000}{6} \approx 133{,}333 \]
This gives one definite value of \(A\), so Statement I alone is sufficient.

Step 3: Test Statement II alone.
Statement II gives a single data point: when \(A = 15{,}000\), \(S = 290{,}000\). Since the slope of Rs. 6 per rupee is already fixed by the question, this one point pins down \(S_0\):
\[ 290{,}000 = S_0 + 6(15{,}000) = S_0 + 90{,}000 \implies S_0 = 200{,}000 \]
This is exactly the same intercept found from Statement I, so Statement II alone also fixes the full equation and lets us solve for \(A\). Statement II alone is sufficient.

Step 4: Compare the two statements.
Each statement, taken alone, is enough to fix the linear sales equation and answer the question. Neither statement needs the other.

Final Answer:
Since either statement alone is sufficient, the correct choice is D. \[ \boxed{D} \]