Rohan is asked to figure out the marks scored by Sunil in three different subjects with the help of certain clues. He is told that the product of the marks obtained by Sunil is 72 and the sum of the marks obtained by Sunil is equal to the Rohan's current age ( in completed years). Rohan could not answer the question with this information. When he was also told that Sunil got the highest marks in Physics among the three subjects, he immediately answered the question correctly. What is the sum of the marks scored by Sunil in the two subjects other than Physics?

Options

A. 6
B. 8
C. 10
D. cannot be determined

Answer

To solve the problem, we need to find the marks scored by Sunil in three subjects such that:

1. The product of the marks is 72.
2. The sum of the marks equals Rohan's current age.
3. The highest marks are in Physics.

Let's break down the solution step by step.

### Step 1: Identify the factors of 72
We need to find sets of three numbers (marks) whose product is 72. The possible combinations of three factors of 72 are:
- 1, 1, 72
- 1, 2, 36
- 1, 3, 24
- 1, 4, 18
- 1, 6, 12
- 1, 8, 9
- 2, 2, 18
- 2, 3, 12
- 2, 4, 9
- 2, 6, 6
- 3, 3, 8
- 3, 4, 6

### Step 2: Calculate the sums of the combinations
Next, we calculate the sums of these combinations to see which ones could correspond to Rohan's age:
- 1 + 1 + 72 = 74
- 1 + 2 + 36 = 39
- 1 + 3 + 24 = 28
- 1 + 4 + 18 = 23
- 1 + 6 + 12 = 19
- 1 + 8 + 9 = 18
- 2 + 2 + 18 = 22
- 2 + 3 + 12 = 17
- 2 + 4 + 9 = 15
- 2 + 6 + 6 = 14
- 3 + 3 + 8 = 14
- 3 + 4 + 6 = 13

### Step 3: Analyze the information given
Rohan could not determine the marks with just the product and sum. This implies that there must be at least two combinations that give the same sum. Looking at our sums, we see that:
- The sum of 14 appears twice:
- From the combination (2, 6, 6)
- From the combination (3, 3, 8)

### Step 4: Use the additional clue
We are told that the highest marks are in Physics. Therefore, we need to choose the combination where the highest mark is distinct and can be identified as Physics.

From the combinations:
- (2, 6, 6): The highest mark is 6, which is not distinct.
- (3, 3, 8): The highest mark is 8, which is distinct.

Thus, the marks must be 3, 3, and 8, where 8 is the highest in Physics.

### Step 5: Calculate the sum of the other two subjects
Now, we need to find the sum of the marks in the two subjects other than Physics:
- Marks in Physics = 8
- Marks in the other two subjects = 3 and 3

Sum of the other two subjects = 3 + 3 = 6.

### Final Answer
The sum of the marks scored by Sunil in the two subjects other than Physics is **6**.

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