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Direction: The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.
Arun and Bhadra are brothers. In how many years from now will Bhadra's age be 50 years?
I. The ratio of the present ages of Arun and Bhadra is 5:7 respectively.
II. Bhadra was born 10 years before Arun.
III. 5 years hence, Arun's age would be three-fourths of Bhadra's age at that time.

A

Any two of the three

B

Only II and either I or III

C

All I, II and III

D

Only II and III

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of determining in how many years Bhadra's age will be 50, we will analyze the provided statements step by step. ### Step 1: Understand the Question We need to find out how many years from now Bhadra will be 50 years old. ### Step 2: Analyze Statement I **Statement I:** The ratio of the present ages of Arun and Bhadra is 5:7. Let the present age of Arun be \(5x\) and the present age of Bhadra be \(7x\). ### Step 3: Analyze Statement II **Statement II:** Bhadra was born 10 years before Arun. This means if Arun's present age is \(5x\), then Bhadra's present age \(7x\) should satisfy the equation: \[ 7x = 5x + 10 \] Solving this gives: \[ 2x = 10 \implies x = 5 \] Thus, Arun's age is \(5 \times 5 = 25\) years, and Bhadra's age is \(7 \times 5 = 35\) years. ### Step 4: Determine Years Until Bhadra is 50 Bhadra is currently 35 years old. To find out how many years until he is 50: \[ 50 - 35 = 15 \text{ years} \] ### Step 5: Analyze Statement III **Statement III:** 5 years hence, Arun's age would be three-fourths of Bhadra's age at that time. In 5 years, Arun's age will be \(25 + 5 = 30\) years, and Bhadra's age will be \(35 + 5 = 40\) years. We check: \[ \frac{3}{4} \times 40 = 30 \] This statement is also true and consistent with our previous calculations. ### Conclusion From the analysis, we see that we can derive Bhadra's age and the number of years until he is 50 using either the first and second statements or the second and third statements. Therefore, any two of the three statements are sufficient to answer the question. ### Final Answer The answer is that we can conclude the answer from any two of the three statements.
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