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The sum of the ages of Chetan and Ravi is equal to the age of their grandmother. 8 years ago, Ravi was 1/4 times as old as his grandmother’s present age and 4 years later he will be 3/8 times as old as her present age. What will be the ratio of the age of Ravi to that of Chetan after 8 years?
- a)4 : 7
- b)2 : 3
- c)5 : 9
- d)7 : 11
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The sum of the ages of Chetan and Ravi is equal to the age of their gr...
Given Information:
- The sum of the ages of Chetan and Ravi is equal to the age of their grandmother.
- 8 years ago, Ravi was 1/4 times as old as his grandmother's present age.
- 4 years later, Ravi will be 3/8 times as old as his grandmother's present age.
Solving the Problem:
To solve this problem, let's first assign variables to the ages of Chetan, Ravi, and their grandmother:
- Let the age of Chetan be C years.
- Let the age of Ravi be R years.
- Let the age of their grandmother be G years.
Now, we can write the following equations based on the given information:
1. C + R = G (Sum of Chetan and Ravi's ages is equal to their grandmother's age)
2. R - 8 = (1/4)G (8 years ago, Ravi was 1/4 times as old as his grandmother's present age)
3. R + 4 = (3/8)G (4 years later, Ravi will be 3/8 times as old as his grandmother's present age)
Solving these equations simultaneously, we get:
G = 64 years, R = 24 years, and C = 40 years.
Calculating the Ratio of Ravi's and Chetan's Ages after 8 years:
After 8 years, Ravi's age will be 24 + 8 = 32 years, and Chetan's age will be 40 + 8 = 48 years.
Therefore, the ratio of Ravi's age to Chetan's age after 8 years is:
Ravi's age : Chetan's age = 32 : 48 = 2 : 3
Thus, the correct answer is option (b) 2 : 3.
- The sum of the ages of Chetan and Ravi is equal to the age of their grandmother.
- 8 years ago, Ravi was 1/4 times as old as his grandmother's present age.
- 4 years later, Ravi will be 3/8 times as old as his grandmother's present age.
Solving the Problem:
To solve this problem, let's first assign variables to the ages of Chetan, Ravi, and their grandmother:
- Let the age of Chetan be C years.
- Let the age of Ravi be R years.
- Let the age of their grandmother be G years.
Now, we can write the following equations based on the given information:
1. C + R = G (Sum of Chetan and Ravi's ages is equal to their grandmother's age)
2. R - 8 = (1/4)G (8 years ago, Ravi was 1/4 times as old as his grandmother's present age)
3. R + 4 = (3/8)G (4 years later, Ravi will be 3/8 times as old as his grandmother's present age)
Solving these equations simultaneously, we get:
G = 64 years, R = 24 years, and C = 40 years.
Calculating the Ratio of Ravi's and Chetan's Ages after 8 years:
After 8 years, Ravi's age will be 24 + 8 = 32 years, and Chetan's age will be 40 + 8 = 48 years.
Therefore, the ratio of Ravi's age to Chetan's age after 8 years is:
Ravi's age : Chetan's age = 32 : 48 = 2 : 3
Thus, the correct answer is option (b) 2 : 3.
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Community Answer
The sum of the ages of Chetan and Ravi is equal to the age of their gr...
Let the age of the grandmother = 8x
Difference = 3x – 2x = (8 + 4)
x = 12
Age of Grandmother = 8 × 12 = 96 years
Age of Ravi = 2x + 8 = 32 years
Age of Chetan = 96 – 32 = 64 years
Reqd. ratio = (32 + 8) : (64 + 8) = 40 : 72 = 5 : 9
Hence, option C is correct.
Difference = 3x – 2x = (8 + 4)
x = 12
Age of Grandmother = 8 × 12 = 96 years
Age of Ravi = 2x + 8 = 32 years
Age of Chetan = 96 – 32 = 64 years
Reqd. ratio = (32 + 8) : (64 + 8) = 40 : 72 = 5 : 9
Hence, option C is correct.
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The sum of the ages of Chetan and Ravi is equal to the age of their grandmother. 8 years ago, Ravi was 1/4 times as old as his grandmother’s present age and 4 years later he will be 3/8 times as old as her present age. What will be the ratio of the age of Ravi to that of Chetan after 8 years?a)4 : 7b)2 : 3c)5 : 9d)7 : 11Correct answer is option 'C'. Can you explain this answer?
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