Sum of the ages of a father and son is 45 years. Five years, ago product of their ages was 4 times the father’s age at that time. Present ages of father and his son, respectively are:a)25,10b)36,9c)39,6d)20,5e)NoneCorrect answer is option 'B'. Can you explain this answer?

Question

Sum of the ages of a father and son is 45 years. Five years, ago product of their ages was 4 times the father&#8217;s age at that time. Present ages of father and his son, respectively are:a)25,10b)36,9c)39,6d)20,5e)NoneCorrect answer is option 'B'. Can you explain this answer?

Accepted Answer

Let sons age = x years. Then fathers age = (45 - x)years.

(x—5)(45—x—5) = 4(45- x - 5) hence (x—5) = 4 so x = 9

Their ages are 36 years and 9 years.

Answer

Let father's age is x then son's age is (45-x) again according to question, five years ago ,sum of their ages is 4 times the sum of age of father at that time then, (x-5)×(45-x-5)=4(x-5) solve it x=father's age is 36 and son'S age 9

Answer

Let the present age of the father be x

∴ The present age of the son is (45−x)

Five years ago Age of father =(x−5)
Age of son =((45−x)−5)=(40−x)

⇒(x−5)(40−x)=4×(x−5)
⇒40x−200−x2+5x=4x−20
⇒x2−41x+180=0
⇒(x−36)(x−5)=0

⇒x=36 or x=5 (Not possible)
∴x=36 years

∴ Present age of father =36 years

∴ Present age of son =45−36=9 years

So, the correct answer is B.

Answer

Problem Analysis:
Let the present age of father and son be F and S respectively.
Given, F + S = 45
Also, 5 years ago, (F-5)(S-5) = 4(F-5)
Simplifying, we get F*S - 5F - 4S + 20 = 0

Solution:
To solve this problem, we can use the following steps:

1. Use the first equation to express one variable in terms of the other, say F = 45 - S.
2. Substitute F in the second equation to get an equation in terms of S only.
3. Solve the resulting quadratic equation to get the value of S.
4. Use the value of S to find the value of F.
5. Check the answer by verifying that the conditions are satisfied.

Detailed Solution:
1. F + S = 45
F = 45 - S

2. (45-S)*S - 5(45-S) - 4S + 20 = 0
Simplify the above equation
S^2 - 6S - 25 = 0

3. Solve the quadratic equation using the quadratic formula.
S = (6 ± sqrt(6^2 - 4*1*(-25))) / 2
S = (6 ± sqrt(136)) / 2
S = 9 or S = -4.67 (rejected)

4. Use the value of S to find F.
F = 45 - S
When S = 9, F = 36

5. Verify that the answer satisfies the conditions.
Five years ago, F-5 = 31 and S-5 = 4
Product of their ages 5 years ago was 31 * 4 = 124
Father's age 5 years ago was 31
4 times the father's age 5 years ago was 4 * 31 = 124

So, the answer is (B) 36, 9.

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