The sum of the age of a father and his son is 45 years. Five years ago, the product of their ages was four times the age of the father at that time. What is the present age of the father and son?

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KPTCL Assistant Exam (Mescom) SLOT-1 7-MAY­-2017 click here to view all questions

The sum of the age of a father and his son is 45 years. Five years ago, the product of their ages was four times the age of the father at that time. What is the present age of the father and son?

A9, 36

B11, 34

C4, 41

D6, 39

rahul ? Jan 26 '2020 at 10:24

Let's denote the present age of the father as $F$ and the present age of the son as $S$. According to the given information: 1. The sum of the age of the father and his son is 45 years: $$F + S = 45$$ 2. Five years ago, the product of their ages was four times the age of the father at that time. This can be expressed as: $$(F - 5)(S - 5) = 4(F - 5)$$ Now, let's solve this system of equations. From equation 1, we can express the present age of the father in terms of the son's age: $$F = 45 - S$$ Substitute this expression for $F$ in equation 2: $$(45 - S - 5)(S - 5) = 4(45 - S - 5)$$ $$= (40 - S)(S - 5) = 4(40 - S)$$ Expanding both sides: $$40S - 5S - 200 + 5S = 160 - 4S$$ $$35S - 200 = 160 - 4S$$ $$35S + 4S = 160 + 200$$ $$39S = 360$$ $$S = \frac{360}{39}$$ $$S = 9.23$$ Now that we have the age of the son, we can find the age of the father using the equation: $$F = 45 - S$$ $$F = 45 - 9.23$$ $$F \approx 35.77$$ Since ages are typically considered in whole numbers, we round the ages: The present age of the son is approximately 9 years, and the present age of the father is approximately 36 years.

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Let's denote the present age of the father as $F$ and the present age of the son as $S$. According to the given information: 1. The sum of the age of the father and his son is 45 years: $$F + S = 45$$ 2. Five years ago, the product of their ages was four times the age of the father at that time. This can be expressed as: $$(F - 5)(S - 5) = 4(F - 5)$$ Now, let's solve this system of equations. From equation 1, we can express the present age of the father in terms of the son's age: $$F = 45 - S$$ Substitute this expression for $F$ in equation 2: $$(45 - S - 5)(S - 5) = 4(45 - S - 5)$$ $$= (40 - S)(S - 5) = 4(40 - S)$$ Expanding both sides: $$40S - 5S - 200 + 5S = 160 - 4S$$ $$35S - 200 = 160 - 4S$$ $$35S + 4S = 160 + 200$$ $$39S = 360$$ $$S = \frac{360}{39}$$ $$S = 9.23$$ Now that we have the age of the son, we can find the age of the father using the equation: $$F = 45 - S$$ $$F = 45 - 9.23$$ $$F \approx 35.77$$ Since ages are typically considered in whole numbers, we round the ages: The present age of the son is approximately 9 years, and the present age of the father is approximately 36 years. rahul ? answered Jan 26 '2020 at 10:24 All Comments

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