Mother is 25 years older than her son. Find the age of the son if, after 8 years, the ratio of son’s age to mother’s age will be \[\dfrac{4}{9}\].
Answer
361.5k+ views
Hint: Assign variables to mother’s age and son’s age. Write the equations relating to their age in the present and after 8 years and solve them to find the son’s age.
Complete step by step answer:
Let the present age of the mother be x years and the present age of the son be y years.
It is given that a mother is 25 years older than her son. Then, we have:
\[x = y + 25............(1)\]
After eight years, the ratio of son’s age to the mother’s age is 4:9. We know that the age of the mother after 8 years is (x + 8) and the age of the son after 8 years is (y + 8). Hence, we have:
\[\dfrac{{y + 8}}{{x + 8}} = \dfrac{4}{9}............(2)\]
We now have two equations with two unknowns, hence, we substitute equation (1) in equation (2), to obtain the age of the son.
\[\dfrac{{y + 8}}{{(y + 25) + 8}} = \dfrac{4}{9}\]
Simplifying the term in the denominator, we get:
\[\dfrac{{y + 8}}{{y + 33}} = \dfrac{4}{9}\]
Cross-multiplying, we get:
\[9(y + 8) = 4(y + 33)\]
Multiplying inside the brackets, we obtain:
\[9y + 72 = 4y + 132\]
Taking all terms containing y to the left-hand side and all constant terms to the right hand side, we have:
\[9y - 4y = 132 - 72\]
Simplifying, we get:
\[5y = 60\]
Solving for y, we get:
\[y = \dfrac{{60}}{5}\]
\[y = 12\]
Hence, the present age of the son is 12 years.
Note: After you obtain the age of the son, find the age of the mother and substitute in the equations to check if the answer is correct. The key in such questions is to translate the statements of the problem into mathematical statements.
Complete step by step answer:
Let the present age of the mother be x years and the present age of the son be y years.
It is given that a mother is 25 years older than her son. Then, we have:
\[x = y + 25............(1)\]
After eight years, the ratio of son’s age to the mother’s age is 4:9. We know that the age of the mother after 8 years is (x + 8) and the age of the son after 8 years is (y + 8). Hence, we have:
\[\dfrac{{y + 8}}{{x + 8}} = \dfrac{4}{9}............(2)\]
We now have two equations with two unknowns, hence, we substitute equation (1) in equation (2), to obtain the age of the son.
\[\dfrac{{y + 8}}{{(y + 25) + 8}} = \dfrac{4}{9}\]
Simplifying the term in the denominator, we get:
\[\dfrac{{y + 8}}{{y + 33}} = \dfrac{4}{9}\]
Cross-multiplying, we get:
\[9(y + 8) = 4(y + 33)\]
Multiplying inside the brackets, we obtain:
\[9y + 72 = 4y + 132\]
Taking all terms containing y to the left-hand side and all constant terms to the right hand side, we have:
\[9y - 4y = 132 - 72\]
Simplifying, we get:
\[5y = 60\]
Solving for y, we get:
\[y = \dfrac{{60}}{5}\]
\[y = 12\]
Hence, the present age of the son is 12 years.
Note: After you obtain the age of the son, find the age of the mother and substitute in the equations to check if the answer is correct. The key in such questions is to translate the statements of the problem into mathematical statements.
Last updated date: 29th Sep 2023
•
Total views: 361.5k
•
Views today: 10.61k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

How many millions make a billion class 6 maths CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

What is the past tense of read class 10 english CBSE

How many crores make 10 million class 7 maths CBSE

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
