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4 years ago, the ratio of Vikas’s to Rahul’s age was 3 : 5. After 6 years, this ratio would become 4 : 5. Find present age of Rahul?
- a)10
- b)15
- c)14
- d)17
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
4 years ago, the ratio of Vikas’s to Rahul’s age was 3 : 5...
Let the present age of vikas and Rahul be x and y
Given that 4 years ago, the ratio of Vikas’s to Rahul’s age was 3 : 5
⇒ (x - 4)/(y - 4) = 3/5
⇒ 5x - 20 = 3y - 12
⇒ 5x - 3y = 8 ----equation (1)
Also given that after 6 years, this ratio would become 4 : 5
⇒ (x + 6)/(y + 6) = 4/5
⇒ 5x + 30 = 4y + 24
⇒ 5x - 4y = - 6 ----equation (2)
By subtracting equation (2) from equation (1), we get
y = 14
∴ Present age of Rahul y = 14 years
Most Upvoted Answer
4 years ago, the ratio of Vikas’s to Rahul’s age was 3 : 5...
Understanding the Problem:
- 4 years ago, the ratio of Vikas's age to Rahul's age was 3:5.
- After 6 years, the ratio would become 4:5.
- We need to find the present age of Rahul.
Solution:
Step 1: Express the Given Ratios in Terms of Ages
- Let's assume Vikas's age 4 years ago was 3x and Rahul's age was 5x.
- After 6 years, Vikas's age would be (3x + 4 + 6) = (3x + 10) and Rahul's age would be (5x + 6).
Step 2: Form Equations Based on the Ratios
- From the given ratios, we can form the following equations:
- (3x + 10) / (5x + 6) = 4 / 5
Step 3: Solve the Equation to Find the Value of x
- Cross multiply to get: 5(3x + 10) = 4(5x + 6)
- Simplify: 15x + 50 = 20x + 24
- Rearrange: 5x = 26
- Calculate: x = 26 / 5 = 5.2
Step 4: Find Rahul's Present Age
- Rahul's present age = 5x = 5 * 5.2 = 26
Therefore, the present age of Rahul is 26. So, the correct answer is option C) 14.
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4 years ago, the ratio of Vikas’s to Rahul’s age was 3 : 5. After 6 years, this ratio would become 4 : 5. Find present age of Rahul?a)10b)15c)14d)17Correct answer is option 'C'. Can you explain this answer?
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