Question

13) The sum of the ages of Sanjay and Vijay is thrice the sum of their
ages 5 years ago. What is the product of their present ages, if the sum of
the squares of their ages 5 years ago was 100?
B. 25
C. 50
D. 6.25
A. 12.5​

Answer 1

Answer:

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Answer 2

Given:

• 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 A. 12.5 .