Problems on Ages

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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Saturday, January 25, 2020

Rajesh and Kiran differ in age by 16 years. Rajesh is elder to Kiran. If eight years ago, Rajesh was three times the age of Kiran, find their current ages.

January 25, 2020 |

General Aptitude, KPTCL Assistant Exam (Mescom) SLOT-3 2017, Problems on Ages, UnSolved

Rajesh and Kiran differ in age by 16 years. Rajesh is elder to Kiran. If eight years ago, Rajesh was three times the age of Kiran, find their current ages.

A10, 26

B12, 28

C14, 30

D16, 32

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