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Q.

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?


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a

Present age of Jacob: 50 years and Present age of Jacob's son: 15 years

b

Present age of Jacob: 50 years and Present age of Jacob's son: 10 years

c

Present age of Jacob: 40 years and Present age of Jacob's son: 10 years

d

Present age of Jacob: 35 years and Present age of Jacob's son: 15 years 

answer is C.

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Detailed Solution

Concept- For this type of age problem, we first let the ages of the given people be 'x' and 'y,' and then find their ages first according to given hence years and forming an equation according to given condition, and then find their ages according to given years ago and forming an equation according to given condition. Finally, solve these two equations to discover the values of 'x' and 'y', as well as the needed answer to the provided issue.
Let present age of Jacob is Question Image years
Jacob's son's current age = y years old
Age of Jacob five years hence will be Question Image years
Age of Jacob's five years hence will be Question Image years
Then, according to the question. We have
Jacob's age is three times his son's age five years after him.
Therefore, we have:
Question ImageQuestion ImageQuestion ImageQuestion ImageAlso, age of Jacob five years ago Question Image years
Age of Jacob's son five years ago Question Image years
But according to the question 5 years ago, Jacob's age is seven times his son's age.
So, we have
Question ImageQuestion ImageQuestion ImageSubtracting (ii) from (i) we have
Question ImageQuestion ImageQuestion ImageQuestion ImageSubstituting value of Question Image in equation (i) we have:
Question ImageQuestion ImageQuestion ImageQuestion ImageTherefore, from above we see that the present age of Jacob is 40 years and the present age of Jacob's son is 10 years.
Hence, the correct answer is option 3.
 
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