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The respective ratio between the present ages of Ram and Rakesh is 6 : 11. Four years ago, the ratio of their ages was 1 : 2, respectively. What will be Rakesh's age after five years?  
  • a)
    45 yr 
  • b)
    29 yr 
  • c)
    49 yr 
  • d)
    Cannot be determined 
  • e)
    None of these 
Correct answer is option 'C'. Can you explain this answer?
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The respective ratio between the present ages of Ram and Rakesh is 6 :...
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The respective ratio between the present ages of Ram and Rakesh is 6 :...
Given:
- The ratio between the present ages of Ram and Rakesh is 6:11.
- Four years ago, the ratio of their ages was 1:2.

To find:
- Rakesh's age after five years.

Solution:

Let's assume the present age of Ram as 6x and the present age of Rakesh as 11x.

Four years ago, Ram's age would be (6x - 4) and Rakesh's age would be (11x - 4).
According to the given information, the ratio of their ages four years ago was 1:2.
So, we have the equation:
(6x - 4)/(11x - 4) = 1/2

Simplifying the equation:
2(6x - 4) = 1(11x - 4)
12x - 8 = 11x - 4
12x - 11x = -4 + 8
x = 4

So, Ram's present age is 6x = 6*4 = 24 years.
And Rakesh's present age is 11x = 11*4 = 44 years.

To find Rakesh's age after five years, we add 5 to his present age:
Rakesh's age after five years = 44 + 5 = 49 years.

Therefore, the correct answer is option 'C' - 49 years.
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