Question

The present age of A is twice that of B . After 30 years , age of A will be 1.5 times of age of B . Find the age of A and B ?
A)A = 34 years , B = 17 years
B)A = 30 years , B = 15 years
C)A = 20 years , B = 10 years
D)A = 40 years , B = 20 years

Answer 1

Step-by-step explanation:

As per the provided information in the given question, we have :

• Present age of A is twice that of B.
• After 30 years ,age of A will be 1.5 times of age of B. $\;$

We've been asked to calculate the present age of A and B.

In order to tackle this question, firstly let's assume the present age of B as X years. Now, we'll write the age of A in the terms of the age of B. According to the question, the present age of A is twice the age of B, so his age will be 2X years. Writing their ages in the form of linear equations,

⠀⠀⠀⠀★ A's present age = 2X years

⠀⠀⠀⠀★ B's present age = X years

Also, according to the question; after 30 years, the age of A will be 1.5 times of age of B.

» ⠀After 30 years :

⠀⠀⠀⠀★ A's age = (2X + 30) years

⠀⠀⠀⠀★ B's age = (X + 30) years

Now, we have been given that after 30 years, the age of A will be 1.5 times of age of B. Writing it in the form of a linear equation,

↠⠀⠀A's age = 1.5( B's age )

Substitute the ages of A and B after 30 years.

↠⠀⠀(2X + 30) = 1.5( X + 30 )

Now, using the distributive property, performing multiplication in RHS i.e, multiplying 1.5 with each term of the binomial ( X + 30 ).

↠⠀⠀2X + 30 = 1.5X + 45

Transposing the like terms. Here 2X and 1.5X ; 30 and 45 are like terms. Whenever the terms are transposed, their signs get changed.

↠⠀⠀2X – 1.5X = 45 – 30

Performing subtraction on both sides.

↠⠀⠀0.5X = 15

Transposing 0.5 from LHS to RHS.

↠⠀⠀X = 15 ÷ 0.5

Dividing 15 by 0.5 in RHS.

↠⠀⠀X = 30

⠀⠀⠀⠀_______________________________⠀⠀⠀⠀⠀

❝ Present ages of A and B : ❞

• A's present age = 2X years = 2(30) years = 60 years
• B's present age = X years = 30 years

Answer 2

Answer: None of the above. (As per condition.)

Explanation:

As per question,

1. A = 2B
2. A + 30 = 3/2(B + 30)

By putting A = 2B in second equation,

2B + 30 = 3/2 B + 45

=> 2B - 3/2 B = 45 - 30 = 15

=> 1/2 B = 15

=> B = 30

Therefore, A's age = 60 y/o and that of B's = 30 y/o.