Aptitude - Profit and Loss - Discussion
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
What was the percentage of discount given? | |
I. | 23.5% profit was earned by selling an almirah for Rs. 12,350. |
II. | If there were no discount, the earned profit would have been 30%. |
III. | The cost price of the almirah was Rs. 10,000. |
I. S.P. = Rs. 12350, Gain = 23.5%
 C.P. = Rs. |
 |
100 | x 12350 |  |
= Rs. 10,000. |
| 123.5 |
II. M.P. = 130% of C.P. = 130% of Rs. 10,000 = Rs. 13,000.
From I and II, discount = Rs. (13000 - 12350) = Rs. 650.
| Discount % = | |
650 | x 100 | % = 5%. |
|
| 13000 |
Thus, I and II give the answer.
II and III can not give the answer. Because we require profit percentage with discount and profit percentage without discount. So II and III are not sufficient.
Since III gives C.P. = Rs. 10,000, I and III give the answer.
Therefore, I and II [or] I and III give the answer.
Correct answer is (E).
Let's break down the reasoning and pinpoint the mistake in the provided explanation.
**Correct Analysis**
The goal is to find the discount percentage, which requires the **Selling Price (SP)** and the **Marked Price (MP)**.
1. **Statement I** gives us the **SP = Rs. 12,350**. It also allows us to calculate the Cost Price (CP) since the profit was 23.5%.
$$CP = frac{SP}{1 + (t{Profit}% / 100)} = frac{12,350}{1.235} = {Rs. } 10,000$$.
2. **Statement II** tells us what the profit *would have been* without a discount. This information is used to find the **MP**.
$$MP = CP times (1 + 0.30) = 1.3 times CP$$.
3. **Statement III** gives us the **CP = Rs. 10,000**.
Combining I and II is Sufficient:
As the explanation correctly shows in its first few steps, using I and II together allows us to find all necessary values:
* From I: SP = Rs. 12,350.
* From I, we calculate **CP = Rs. 10,000.
* Using this CP with statement II, we find **MP = $1.3 times 10,000 = {Rs. } 13,000$**.
Since we have both SP and MP, we can calculate the discount. This combination works.
*Conclusion*
* The combination **(I and II)** is sufficient.
* The combination **(I and III)** is not sufficient.
* The combination **(II and III)** is not sufficient (it gives MP and CP, but not SP).
Since only the combination **(I and II)** is sufficient to answer the question, and this is listed as option (A), that is the correct choice.
The correct explanation is; 1 and 2 OR 1, 2 and 3 can give us the answer (either 1 or 3 can be redundant). The option 'ONLY' 1 and 2 is hence wrong.
IIIrd statement is redundant, we can solve this problem using statement I & II or I, II & III.
But they had asked the necessary statements required to answer the question, so I & II are sufficient to answer the question. Therefore option A should be the answer.