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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 ...
To solve this problem, we can start by assigning variables to the present ages of the son, father, and mother. Let's call the present age of the son 's', the father 'f', and the mother 'm'.
Given information:
- The ratio of the present ages of the son and his father is 1:5, so we can write this as s:f = 1:5.
- The ratio of the present ages of the mother and father is 4:5, so we can write this as m:f = 4:5.
- After 2 years, the ratio of the age of the son to that of his mother becomes 3:10.
Using these ratios, we can set up equations to solve for the present ages. Let's start by finding the values of s, f, and m.
Finding the values of s, f, and m:
1. From the first given ratio, we can write s/f = 1/5. Cross-multiplying gives us s = f/5.
2. From the second given ratio, we can write m/f = 4/5. Cross-multiplying gives us m = 4f/5.
Finding the values of s and m after 2 years:
1. After 2 years, the son's age will be s + 2 and the mother's age will be m + 2.
Setting up the equation using the third given ratio:
The ratio of the son's age to the mother's age after 2 years is 3:10. We can write this as (s + 2)/(m + 2) = 3/10.
Substituting the values of s and m from earlier:
(s + 2)/(m + 2) = 3/10
(f/5 + 2)/(4f/5 + 2) = 3/10
(10f + 50)/(20f + 10) = 3/10
Cross-multiplying gives us 30f + 150 = 60f + 30.
Simplifying the equation:
30f - 60f = 30 - 150
-30f = -120
f = 4.
Therefore, the present age of the father is 4 years. So, the correct answer is option 'D'.
Given information:
- The ratio of the present ages of the son and his father is 1:5, so we can write this as s:f = 1:5.
- The ratio of the present ages of the mother and father is 4:5, so we can write this as m:f = 4:5.
- After 2 years, the ratio of the age of the son to that of his mother becomes 3:10.
Using these ratios, we can set up equations to solve for the present ages. Let's start by finding the values of s, f, and m.
Finding the values of s, f, and m:
1. From the first given ratio, we can write s/f = 1/5. Cross-multiplying gives us s = f/5.
2. From the second given ratio, we can write m/f = 4/5. Cross-multiplying gives us m = 4f/5.
Finding the values of s and m after 2 years:
1. After 2 years, the son's age will be s + 2 and the mother's age will be m + 2.
Setting up the equation using the third given ratio:
The ratio of the son's age to the mother's age after 2 years is 3:10. We can write this as (s + 2)/(m + 2) = 3/10.
Substituting the values of s and m from earlier:
(s + 2)/(m + 2) = 3/10
(f/5 + 2)/(4f/5 + 2) = 3/10
(10f + 50)/(20f + 10) = 3/10
Cross-multiplying gives us 30f + 150 = 60f + 30.
Simplifying the equation:
30f - 60f = 30 - 150
-30f = -120
f = 4.
Therefore, the present age of the father is 4 years. So, the correct answer is option 'D'.
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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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