Last month, a company decided to increase the price of its mixer by 10 percent. What is the present price of the mixer? Statement I: One month ago, the total cost of a mixer and a juicer together was Rs 2850. Statement II: The amount of 10 percent increase on the mixer comes to Rs 220.

Introduction / Context:
This data sufficiency problem involves percentage increase and basic arithmetic. The company has increased the price of a mixer by 10 percent and we are asked to compute the present price of the mixer. Two statements are given: one about the combined cost of a mixer and a juicer before the increase, and another about the absolute rupee amount of the 10 percent increase. We must determine which statements are sufficient to uniquely find the current price.

Given Data / Assumptions:

• The mixer price was raised by 10 percent last month.
• We need the present price after the 10 percent increase.
• Statement I: Earlier, the sum of the prices of one mixer and one juicer was Rs 2850.
• Statement II: The absolute amount of the 10 percent increase for the mixer is Rs 220.
• Prices are in rupees and percentage is calculated on the earlier price.

Concept / Approach:
The key concept is the relation between percentage increase and absolute increase. If the increase is 10 percent and the absolute increase is known, we can find the original price by the formula: increase = original_price * (percentage / 100) Once we have the original price, the new price is: new_price = original_price + increase Data sufficiency requires us to check if any statement alone or both together provide enough numeric information to apply this logic.

Step-by-Step Solution:
Step 1: Consider statement I. Let the earlier price of the mixer be M and the earlier price of the juicer be J. Statement I tells us that M + J = 2850. Step 2: From statement I alone we cannot find M, because J is unknown and there is only one equation with two unknowns. So statement I alone is not sufficient. Step 3: Now consider statement II. The amount of 10 percent increase on the mixer is Rs 220. Step 4: Use the percentage formula. If original_price is M, then 10 percent of M equals 220. So we write 0.10 * M = 220. Step 5: Solve this equation: M = 220 / 0.10 = 2200. So the earlier price of the mixer was Rs 2200. Step 6: The present price after a 10 percent increase is original price plus increase. So present_price = 2200 + 220 = Rs 2420. Step 7: Statement II alone gives us the exact original price and hence the present price of the mixer. No other information is required. Step 8: Combining statement I with statement II does not change this, because statement II already gives a complete solution; statement I becomes redundant.

Verification / Alternative check:
We can check whether 10 percent of 2200 is indeed 220. Compute 10 percent as 2200 * 10 / 100 = 220, which matches the given increase. Now verify the new price. Adding the increase to the original price gives 2200 + 220 = 2420. There is no ambiguity because the percentage and the increase amount uniquely fix the original price.

Why Other Options Are Wrong:
Option a is wrong because statement I alone gives only the combined cost of mixer and juicer, not the separate price of the mixer. Option c is wrong because only statement II alone, not statement I alone, is sufficient. Option d is wrong because it claims that both statements are needed, whereas statement II alone already provides the full information needed. Option e is wrong because the data in statement II alone clearly allow us to compute a unique present price.

Common Pitfalls:
One common mistake is to overuse statement I, trying to involve the juicer price when it is actually irrelevant for finding the mixer price, given statement II. Some students also misinterpret the phrase amount of 10 percent increase, mistakenly applying 10 percent to the new price rather than the original price. Another pitfall is to believe that data sufficiency always needs both statements, which is not true. Many questions are designed such that one statement is sufficient on its own, testing whether candidates can correctly apply percentage formulas without unnecessary extra information.

Final Answer:
The earlier price of the mixer was Rs 2200 and the present price after a 10 percent increase is Rs 2420. Correct option: The data in statement II alone are sufficient to answer the question.