Question

By what percentage did the sales of a shop increase? Statement I: Sales rose from Rs. 200 to Rs. 250. Statement II: The increase in sales was Rs. 50.

• A. Statement I alone is sufficient, but Statement II alone is not sufficient.
• B. Statement II alone is sufficient, but Statement I alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Hint:

Remember that a percentage increase needs both the base (original) value and the amount of change - check whether each statement alone supplies both pieces.

Answer 1

The Correct Option is A

Step 1: Instead of just computing the percentage from Statement I, reason about what information a percentage-increase calculation fundamentally requires, then test whether each statement supplies it.
Step 2: A percentage increase is defined as $\frac{\text{increase}}{\text{original value}}\times100$. This formula needs BOTH the amount of increase AND the original (base) value to produce a unique percentage.
Step 3: Statement I: Sales rose from Rs. 200 to Rs. 250. This gives both the original value (Rs. 200) and the increase (Rs. 50), so the percentage is fixed: $\frac{50}{200}\times100=25\%$. Statement I alone IS sufficient.
Step 4: Statement II: The increase in sales was Rs. 50. This gives only the increase amount, with no original value stated. To see this is not enough, imagine the original sales were Rs. 500 instead of Rs. 200: the same Rs. 50 increase would then represent $\frac{50}{500}\times100=10\%$, a completely different percentage.
Step 5: Since Statement II can correspond to many different percentage increases depending on the unstated original value, Statement II alone is NOT sufficient. Only Statement I alone is sufficient. \[\boxed{\text{Statement I alone is sufficient, but Statement II alone is not sufficient.}}\] Correct option: (1) Statement I alone is sufficient, but Statement II alone is not sufficient.