Question

five years ago a was thrice as old as b and ten years later a shall be twice as old as b what are the present ages of a and b​

Answer 1

Answer:

50 and 20 years

Step-by-step explanation:

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

• Five years ago A was three times as old as B.
• Ten years later A shall be two times as old as B.

We've been asked to calculate their present ages.

Let us suppose the age of A as a years and the age of B as b years.

– Now, according to the question, five years ago A was thrice as old as B. According to our assumption,

$\twoheadrightarrow\quad\sf{a-5=3(b-5)}$

Multiplying 3 by b and 5 on RHS.

$\twoheadrightarrow\quad\sf{a-5=3b-15}$

Transposing -5 from LHS to RHS, it's sign gets changed.

$\twoheadrightarrow\quad\sf{a=3b-15+5}$

Performing subtraction.

$\twoheadrightarrow\quad\sf{a=3b-10\qquad\qquad\ \left\lgroup\begin{matrix}\sf{{eq}^{n}\: (1)}\end{matrix}\right\rgroup\]}$

– Now, according to the question, ten years later A shall be twice as old as B. According to our assumption.

$\twoheadrightarrow\quad\sf{a+10=2(b+10)}$

Multiplying 2 by a and 10 on RHS.

$\twoheadrightarrow\quad\sf{a+10=2b+20}$

Transposing +10 from LHS to RHS, it's sign gets changed.

$\twoheadrightarrow\quad\sf{a=2b+20-10}$ Performing subtraction.

$\twoheadrightarrow\quad\sf{a=2b+10\qquad\qquad\ \left\lgroup\begin{matrix}\sf{{eq}^{n}\: (2)}\end{matrix}\right\rgroup\]}$

From eqⁿ 1 and 2, we get:

$\twoheadrightarrow\quad\sf{3b-10=2b+10}$

Transposing -10 from LHS to RHS, it's sign gets changed.

$\twoheadrightarrow\quad\sf{3b=2b+10+10}$

Performing addition.

$\twoheadrightarrow\quad\sf{3b=2b+20}$

Transposing +2b from RHS to LHS, it's sign gets changed.

$\twoheadrightarrow\quad\sf{3b-2b=20}$

Performing subtraction.

$\twoheadrightarrow\quad\underline{\boxed{\bold{b=20\: years}}}$

We have calculated the value of b (Age of B) that is 20 years. As we have assumed that the Age of A is a years and from eqⁿ (1), we get:

$\twoheadrightarrow\quad\sf{a=3b-10}$

Substituting value of b in order to perform multiplication and subtraction.

$\twoheadrightarrow\quad\sf{ a=3(20)-10}$

Performing multiplication.

$\twoheadrightarrow\quad\sf{a=60-10}$

Performing subtraction in order to calculate the age of A.

$\twoheadrightarrow\quad\underline{\boxed{\bold{a=50\: years}}}$

❝ Therefore, age of A is 50 years and age of B is 20 years. ❞