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The ratio of the present ages of a son and his father is 1:5 and that of his mother and father is 4:5. After 2 yrs the ratio of the age of the son to that of his mother becomes 3:10. What is the present age of the father?
- a)30 yrs
- b)28 yrs
- c)37 yrs
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The ratio of the present ages of a son and his father is 1:5 and that ...
Let the present age of Father, Mother and son be x years, y years and z years
Now z/x = 1/5
⇒ x = 5z
⇒ z = 1/5 x
y/x = 4/5
⇒ 4x = 5y
y = 4/5 x
After 2 years
z + 2/y + 2 = 3/10
∴ 10z + 20 = 3y + 6
10 x 1/5 x + 14 = 3 x 4/5 x
2x - 12/5 x = - 14
10x - 12x/5 = - 14
- 2x/5 = -14
x = 70/2 = 35
∴ Father present age is 35 years
Now z/x = 1/5
⇒ x = 5z
⇒ z = 1/5 x
y/x = 4/5
⇒ 4x = 5y
y = 4/5 x
After 2 years
z + 2/y + 2 = 3/10
∴ 10z + 20 = 3y + 6
10 x 1/5 x + 14 = 3 x 4/5 x
2x - 12/5 x = - 14
10x - 12x/5 = - 14
- 2x/5 = -14
x = 70/2 = 35
∴ Father present age is 35 years
Most Upvoted Answer
The ratio of the present ages of a son and his father is 1:5 and that ...
Let the present age of Father, Mother and son be x years, y years and z years
Now z/x = 1/5
⇒ x = 5z
⇒ z = 1/5 x
y/x = 4/5
⇒ 4x = 5y
y = 4/5 x
After 2 years
z + 2/y + 2 = 3/10
∴ 10z + 20 = 3y + 6
10 x 1/5 x + 14 = 3 x 4/5 x
2x - 12/5 x = - 14
10x - 12x/5 = - 14
- 2x/5 = -14
x = 70/2 = 35
∴ Father present age is 35 years
Now z/x = 1/5
⇒ x = 5z
⇒ z = 1/5 x
y/x = 4/5
⇒ 4x = 5y
y = 4/5 x
After 2 years
z + 2/y + 2 = 3/10
∴ 10z + 20 = 3y + 6
10 x 1/5 x + 14 = 3 x 4/5 x
2x - 12/5 x = - 14
10x - 12x/5 = - 14
- 2x/5 = -14
x = 70/2 = 35
∴ Father present age is 35 years
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Community Answer
The ratio of the present ages of a son and his father is 1:5 and that ...
To solve this problem, we can break it down into several steps:
Step 1: Define the variables
Let's assume the present age of the son is S, the present age of the father is F, and the present age of the mother is M.
Step 2: Establish the given ratios
From the given information, we know that:
- The ratio of the present ages of the son and father is 1:5, which can be written as S:F = 1:5.
- The ratio of the present ages of the mother and father is 4:5, which can be written as M:F = 4:5.
Step 3: Solve the first equation
Since S:F = 1:5, we can write S = (1/5)F.
Step 4: Solve the second equation
Since M:F = 4:5, we can write M = (4/5)F.
Step 5: Establish the new ratio after 2 years
After 2 years, the son's age will be S + 2 and the mother's age will be M + 2. The new ratio is given as (S + 2):(M + 2) = 3:10.
Step 6: Substitute the expressions from step 3 and 4 into the new ratio
Substituting S = (1/5)F and M = (4/5)F into the new ratio, we get:
((1/5)F + 2):((4/5)F + 2) = 3:10.
Step 7: Cross-multiply and solve for F
Cross-multiplying the equation from step 6, we get:
10((1/5)F + 2) = 3((4/5)F + 2).
Simplifying this equation, we get:
2F + 20 = 12F + 6.
Bringing like terms together, we have:
10F = 14.
Dividing both sides by 10, we get:
F = 1.4.
Since the age cannot be in decimal, we can conclude that there is an error in the question or the options provided. Therefore, the correct answer cannot be determined.
Therefore, the correct answer is option D) None of these.
Step 1: Define the variables
Let's assume the present age of the son is S, the present age of the father is F, and the present age of the mother is M.
Step 2: Establish the given ratios
From the given information, we know that:
- The ratio of the present ages of the son and father is 1:5, which can be written as S:F = 1:5.
- The ratio of the present ages of the mother and father is 4:5, which can be written as M:F = 4:5.
Step 3: Solve the first equation
Since S:F = 1:5, we can write S = (1/5)F.
Step 4: Solve the second equation
Since M:F = 4:5, we can write M = (4/5)F.
Step 5: Establish the new ratio after 2 years
After 2 years, the son's age will be S + 2 and the mother's age will be M + 2. The new ratio is given as (S + 2):(M + 2) = 3:10.
Step 6: Substitute the expressions from step 3 and 4 into the new ratio
Substituting S = (1/5)F and M = (4/5)F into the new ratio, we get:
((1/5)F + 2):((4/5)F + 2) = 3:10.
Step 7: Cross-multiply and solve for F
Cross-multiplying the equation from step 6, we get:
10((1/5)F + 2) = 3((4/5)F + 2).
Simplifying this equation, we get:
2F + 20 = 12F + 6.
Bringing like terms together, we have:
10F = 14.
Dividing both sides by 10, we get:
F = 1.4.
Since the age cannot be in decimal, we can conclude that there is an error in the question or the options provided. Therefore, the correct answer cannot be determined.
Therefore, the correct answer is option D) None of these.
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The ratio of the present ages of a son and his father is 1:5 and that of his mother and father is 4:5. After 2 yrs the ratio of the age of the son to that of his mother becomes 3:10. What is the present age of the father?a)30 yrsb)28 yrsc)37 yrsd)None of theseCorrect answer is option 'D'. Can you explain this answer?
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