Question

The sum of the ages of Bharat and
Sharat is twice the sum of their ages
seven years ago. What is the product of
their present ages, if the sum of the
squares of their ages is 400?​

Answer 1

Answer:

Here's the answer

Hope it helps

Answer 2

ANSWER:

• Product of their present ages = 192

GIVEN:

• The sum of the ages of Bharat and Sharat is twice the sum of their ages seven years ago.

• The sum of the squares of their ages is 400.

TO FIND:

• Product of their present ages.

EXPLANATION:

Let the age of Bharat be x and the age of Sharat be y.

x + y = 2(x - 7 + y - 7)

x + y = 2(x + y - 14)

x + y = 2x + 2y - 28

x + y - 28 = 0

x + y = 28

x² + y² = 400

$\boxed{\bold{\large{\purple{x^2 + y^2 = (x+y)^2 - 2xy}}}}$

x² + y² = 400

x + y = 28

400 = (28)² - 2xy

400 = 784 - 2xy

- 384 = - 2xy

2xy = 384

xy = 192

Hence the product of their ages is 192.

VERIFICATION:

Substitute x = 28 - y in xy = 192

(28 - y)y = 192

28y - y² = 192

y² - 28y + 192 = 0

By splitting the middle term

y² - 16y - 12y + 192 = 0

y(y - 16) - 12(y - 16) = 0

(y - 16)(y - 12) = 0

y = 16 or y = 12

Lets take age of Sharat be 12

Then age of Bharat = 28 - y = 28 - 12

Age of Bharat = 16

Sum of their ages = 16 + 12 = 28

Product of their ages = 16 × 12 = 192

Sum of square of ages = 16² + 12²

Sum of square of ages = 256 + 144

Sum of square of ages = 400

HENCE VERIFIED.

NOTE: Sharat's age can also be taken as 16.