Ex 3.2 Q3 (vi) - Five years hence, the age of Jacob will be three times that of his son

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.

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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.

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Class 10 Ex 3.2

Ex 3.2 Q3 vi Class 10

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Class 10 Pair Of Linear Equations in Two Variables

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Ex 3.2 Q3 (vi) - Five years hence, the age of Jacob will be three times that of his son

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?

Try This..

❌ Common Mistakes

📝 Related Questions:-

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