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One year ago, the ratio of Sooraj's and Vimal's age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8 . How old is Vimal?
- a)32
- b)34
- c)36
- d)38
- e)40
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
One year ago, the ratio of Sooraj's and Vimal's age was 6 : 7 ...
Let the age of Sooraj and Vimal, 1 year ago, be 6 x and 7 x respectively.
Given that, four years hence, this ratio would become 7 : 8
Given that, four years hence, this ratio would become 7 : 8
Most Upvoted Answer
One year ago, the ratio of Sooraj's and Vimal's age was 6 : 7 ...
Problem Statement:
One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
Solution:
Let's assume that the present age of Sooraj and Vimal is S and V respectively.
Step 1: Formulate equations based on the given information.
- One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively.
(S-1)/(V-1) = 6/7
- Four years hence, this ratio would become 7:8.
(S+4)/(V+4) = 7/8
Step 2: Simplify the equations.
- (S-1)/(V-1) = 6/7
7S-6V = 1
- (S+4)/(V+4) = 7/8
8S-7V = 12
Step 3: Solve for S and V.
- Multiply the first equation by 8 and the second equation by 6.
56S-48V = 8
48S-42V = 72
- Subtract the second equation from the first equation.
8S-6V = -64
- Solve for V.
V = 36
Step 4: Calculate Sooraj's age.
From equation (1),
7S-6V = 1
7S-6(36) = 1
S = 37/7
Step 5: Check the answer.
Four years ago, Sooraj's age was 33 and Vimal's age was 36.
The ratio of their ages was 6:7.
Four years hence, Sooraj's age would be 37 and Vimal's age would be 40.
The ratio of their ages would be 7:8.
Therefore, the answer is option (c) 36.
One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
Solution:
Let's assume that the present age of Sooraj and Vimal is S and V respectively.
Step 1: Formulate equations based on the given information.
- One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively.
(S-1)/(V-1) = 6/7
- Four years hence, this ratio would become 7:8.
(S+4)/(V+4) = 7/8
Step 2: Simplify the equations.
- (S-1)/(V-1) = 6/7
7S-6V = 1
- (S+4)/(V+4) = 7/8
8S-7V = 12
Step 3: Solve for S and V.
- Multiply the first equation by 8 and the second equation by 6.
56S-48V = 8
48S-42V = 72
- Subtract the second equation from the first equation.
8S-6V = -64
- Solve for V.
V = 36
Step 4: Calculate Sooraj's age.
From equation (1),
7S-6V = 1
7S-6(36) = 1
S = 37/7
Step 5: Check the answer.
Four years ago, Sooraj's age was 33 and Vimal's age was 36.
The ratio of their ages was 6:7.
Four years hence, Sooraj's age would be 37 and Vimal's age would be 40.
The ratio of their ages would be 7:8.
Therefore, the answer is option (c) 36.
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