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Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Syam's present age in years?
- a)28
- b)27
- c)26
- d)24
- e)25
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively....
Explanation:
Ratio of the present age of Kiran and Syam = 5 : 4
Let present age of Kiran = 5x
Present age of Syam = 4x
After 3 years, ratio of their ages = 11/9
⇒ ( 5 x + 3 ) / ( 4 x + 3 ) = 11/ 9
⇒ 9 ( 5 x + 3 ) = 11 ( 4 x + 3 )
⇒ 45 x + 27 = 44 x + 33
⇒ x = 33 − 27 = 6
Syam's present age = 4 x = 4 x 6 = 24
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Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively....
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Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively....
Given information:
- Present ages of Kiran and Syam are in the ratio of 5 : 4, respectively.
- Three years hence, the ratio of their ages will become 11 : 9, respectively.
To find:
- Syam's present age.
Solution:
Let's assume the present ages of Kiran and Syam as 5x and 4x respectively (where x is a constant).
Three years hence, Kiran's age will be (5x + 3) and Syam's age will be (4x + 3).
As per the given information, the ratio of their ages after three years will be 11 : 9. Therefore, we can write:
(5x + 3) : (4x + 3) = 11 : 9
Cross-multiplying the above equation, we get:
9(5x + 3) = 11(4x + 3)
Simplifying the above equation, we get:
45x + 27 = 44x + 33
x = 6
Therefore, Syam's present age (4x) is:
4x = 4 * 6 = 24
Hence, the correct answer is option D (24 years).
- Present ages of Kiran and Syam are in the ratio of 5 : 4, respectively.
- Three years hence, the ratio of their ages will become 11 : 9, respectively.
To find:
- Syam's present age.
Solution:
Let's assume the present ages of Kiran and Syam as 5x and 4x respectively (where x is a constant).
Three years hence, Kiran's age will be (5x + 3) and Syam's age will be (4x + 3).
As per the given information, the ratio of their ages after three years will be 11 : 9. Therefore, we can write:
(5x + 3) : (4x + 3) = 11 : 9
Cross-multiplying the above equation, we get:
9(5x + 3) = 11(4x + 3)
Simplifying the above equation, we get:
45x + 27 = 44x + 33
x = 6
Therefore, Syam's present age (4x) is:
4x = 4 * 6 = 24
Hence, the correct answer is option D (24 years).
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