Question

37) The ages of Anitha and Sumitha are 10 years and 12 years respectively. In
how many years time will the product of their ages will be 224
I need the answer

Answer 1

Answer:

after x years product is 224

then (10+x)(12+x)=224

120+10x+12x+x²=224

x²+22x-224+120=0

x²+22x-104=0

x²+26x-4x-104=0

x(x+26)-4(x+26)=0

(x+26)(x-4)=0

x=-26 or x=4

bbut number of years not negative so x=4

so after 4 years product of their ages is 224

Answer 2

Given,

Age of Anitha = 10 years

Age of Sumitha = 12 years

To find,

We have to the years when the product of their ages will be 224.

Solution,

After 4 years the product of the ages of Anitha and Sumitha will be 224.

Let the years when the product of their ages will be 224 be 'x'.

Age of the Anitha after x years = (x+10) years

Age of the Sumitha after x years = (x+12) years

According to the given condition,

(x+10)(x+12) = 224

x² + 12x +10x + 120 = 224

x² + 22 x -104

x² + 26x -4x -104

x(x+26)-4(x+26)

(x+26)(x-4)

x = -26, 4

So, the value of x = 4.

Hence, after 4 years the product of the ages of Anitha and Sumitha will be 224.