Question

The difference between the present ages of P and Q is 8 yrs and the ratio of their present
ages is 2: 3 respectively. What is P's present age?​

Answer 1

★ How to do :-

Here, we are given with the ratio of two humans P and Q respectively. We are said that the age difference between Q and P is 8 years. We are asked to find the present age of P. Here, we use the concept of variables and shifting the numbers from one hand side to the other. This process changes the sign of the particular number. We can find the age of P by multiplying her part of ratio and the value of x. We can also verify the statement by subtracting the ages of P and Q together. So, let's solve!!

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➤ Solution :-

${\tt \leadsto P : Q = 2 : 3}$

The statement says that,

${\tt \leadsto P : Q = 2x : 3x}$

We are given that,

${\tt \leadsto 3x - 2x = 8}$

Subtract the values on LHS.

${\tt \leadsto 1x = 8}$

Shift the number 1 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{8}{1} = 8}$

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Now, we can find the age of P and Q.

Age of P :-

${\tt \leadsto 2x = 2 \times 8}$

Multiply the numbers to get the age of P.

${\tt \leadsto 16 \: \: years}$

Age of Q :-

${\tt \leadsto 3x = 3 \times 8}$

Multiply the numbers to get the age of P.

${\tt \leadsto 24 \: \: years}$

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${\red{\underline{\boxed{\bf So, \: the \: present \: age \: of \: P \: is \: 16 \: years.}}}}$

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Verification :-

${\tt \leadsto 3x - 2x = 8}$

Substitute the values of x.

${\tt \leadsto (3 \times 8) - (2 \times 8) = 8}$

Multiply the numbers on LHS.

${\tt \leadsto 24 - 16 = 8}$

Subtract the values on LHS.

${\tt \leadsto 8 = 8}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!