the sum of the ages of mukunth and vijay is thrice the sum of their ages five years ago . what is the product of their present ages . if the sum of the squares of their ages five years ago 100
Answers
Answer: The sum of the ages of Sanjay and Vijay is thrice the sum of their ages 5 years ago.
The sum of the squares of their ages 5 years ago was 100.
To find: product of their present ages
Step-by-step explanation:
Let the present ages of Sanjay and Vijay are x years and y years respectively.
∴ the sum of their ages is = x + y
Here 5 years ago, the ages of Sanjay and Vijay 5 were (x - 5) years and (y - 5) years respectively.
∴ the sum of their ages 5 years ago were
= x - 5 + y - 5 years = x + y - 10
By the given conditions,
x + y = 3 (x + y - 10)
⇒ x + y = 3x + 3y - 30
⇒ 2x + 2y = 30
⇒ x + y = 15 ... ... ... (1)
Now the sum of the squares of their ages 5 years ago was
= (x - 5)² + (y - 5)²
= x² - 10x + 25 + y² - 10y + 25
[ use (a - b)² = a² - 2ab + b² ]
= x² + y² - 10x - 10y + 50
By the given conditions,
x² + y² - 10x - 10y + 50 = 100
⇒ (x + y)² - 2xy - 10 (x + y) = 100 - 50 = 50
[ use a² + b² = (a + b)² - 2ab ]
⇒ 15² - 2xy - 10 (15) = 50, by (1)
⇒ 225 - 2xy - 150 = 50
⇒ 2xy = 25
⇒ xy = 12.5
Answer:
∴ the product of their present ages is 12.5 .
NOTE: THIS CAN BE A REFERENCE FOR YOUR QUESTION.