Question

Q. 1) The ages of A and B are in th
ratio 3:5. If after 5 years their ages
will be in the ratio 2:3, then the
present age of B (in years ) is_​

Answer 1

Answer:

The required present age of B is 25 years

Step-by-step explanation:

Given :

• The ages of A and B are in the ratio 3:5
• After 5 years, their ages  will be in the ratio 2:3

To find :

the present age of B

Solution :

The ages of A and B are in the ratio 3 : 5. Multiply the ratio by a constant number (say 'x')

So, the present age of A be 3x years and the present age of B be 5x years

After 5 years,

The age of A = (3x + 5) years

The age of B = (5x + 5) years

Their ages  will be in the ratio 2 : 3

   $\tt \dfrac{A's \ age \ after \ 5 \ years}{B's \ age \ after \ 5 \ years}=\dfrac{2}{3} \\\\\\ \sf \dfrac{3x+5}{5x+5}=\dfrac{2}{3}$

 3(3x + 5) = 2(5x + 5)

  9x + 15 = 10x + 10

  10x + 10 - 9x = 15

    x + 10 = 15

   x = 15 - 10

   x = 5

Substitute the value of x,

The present age of A = 3(5) = 15 years

The present age of B = 5(5) = 25 years

Hence, the required present age of B is 25 years

Verification :

• The present age of A = 15 years

• The present age of B = 25 years

Condition - 1 : The ages of A and B are in the ratio 3:5

 15 : 25 = 3 : 5

5(3) : 5(5) = 3 : 5

 3 : 5 = 3 : 5

 LHS = RHS

Condition - 2 : After 5 years their ages  will be in the ratio 2:3

After 5 years,

A's age = 15 + 5 = 20 years

B's age = 25 + 5 = 30 years

20 : 30 = 2 : 3

10(2) : 10(3) = 2 : 3

 2 : 3 = 2 : 3

 LHS = RHS

Hence verified!

Answer 2

Sorry I don't know the answer

Step-by-step explanation:

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