Ex 3.2 Q3 (vi) - 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?
Solution:-Let,
Present age of Jacob = 'x' years
Present age of Jacob's son = 'y' years
Case (i): Five years hence,
*Age of Jacob = (x + 5) years
*Age of Jacob's son = (y + 5) years
➙ Given that, the age of Jacob will be three times that of his son after five years,
∴ x + 5 = 3(y + 5)
∴ x + 5 = 3y + 15
∴ x = 3y + 15 - 5
∴ x = 3y + 10 ------- (i)
Case(ii): Five years ago,
*Age of Jacob = (x - 5) years
*Age of Jacob's son = (y - 5) years
➙ Given that, the age of Jacob was seven times that of his son before five years,
∴ x - 5 = 7(y - 5)
∴ x - 5 = 7y - 35
∴ 3y + 10 - 5 = 7y - 35 ----- { from (i) }
∴ 7y - 3y = 10 - 5 + 35
∴ 4y = 40
∴ y =
40
/
4
∴ y = 10
➙ Putting y = 10 in Eqⁿ(i)
∴ x = 3(10) + 10
∴ x = 30 + 10
∴ x = 40
Therefore,
*Present age of Jacob
= x
= 40 years
*Present age of Jacob's son
= y
= 10 years
Hence,
The present age of Jacob and his son is 40 years and 10 years respectively.
------------------------------------
Try This..
✒ A mother is four times as old as her daughter. In five years, she will be three times as old. What are their present ages?
✒ The sum of the ages of a father and his son is 50 years. Five years ago, the father's age was four times the son’s age. Find their present ages.
✒ Ten years ago, a father was twelve times as old as his son. After ten years, he will be twice as old. Find their present ages.
❌ Common Mistakes
Mistaking "hence" and "ago":▸ Don’t forget to add 5 years for "hence" and subtract 5 for "ago".Wrong equation formation:▸ Carefully read the relationship, who is how many times older?Arithmetic slips:▸ Miscalculating while solving linear equations can ruin it all!Not checking the final answer:▸ Always plug the values back into the original condition to double-check.
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 3.2
Ex 3.2 Q3 vi Class 10
Class 10 Ex 3.2 Q3 vi
Class 10 Chap 3 Ex 3.2 Q3 vi
Class 10 Pair Of Linear Equations in Two Variables
If you found it helpful, please leave a comment below sharing your thoughts or questions.
Don’t forget to share it with your classmates to help them learn too.
Good luck, and happy learning!
Together, let’s make math simpler and more enjoyable for everyone!