Question

The ratio of the ages of a and b at present is 4:5.After one year product of their ages will become 357.Then a's age after 10 years will be

Answer 1

Step-by-step explanation:

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Answer 2

Question -

The ratio of the ages of a and b at present is 4:5.

After one year product of their ages will become 357.

Then a's age after 10 years will be ?

Solution -

In the above question, the following information is given -

The ratio of the ages of a and b at present is 4:5.

After one year product of their ages will become 357.

Let the present ages of A and B be 4x and 5x years respectively.

After 1 year,

Age Of A = 4x + 1 years

Age Of B = 5x + 1 years.

Now the product of their ages is 357.

Hence,

$( 4x + 1)( 5x + 1) = 357 \\ \\20x^2 + 4x + 5x + 1 = 357 \\ \\20x^2 - 9x - 356 = 0 \\ \\ 20x^2 - 89x + 80x - 356 = 0 \\ \\ x( 20x - 89 ) - 4 ( 20x - 89 ) = 0 \\ \\(x - 4)( 20x - 89 ) = 0$

Since, age cannot be a fraction, therefore the only value of x is that x = 4.

The present age of A is equal to 4x .

Hence, present age of A = 16 years.

10  years later,

Age Of A = 26 Years.

Hence the age of A after 10 years is 26 years.

Answer -

The age of A after 10 years is 26 years.