Question

The sum of present ages of p and q is 54 years. after 4 years ,ratio of their ages will be 2:3 .find the present age of p

Answer 1

p+q=54
p=54-q

After 4 years,

P=p+4
q=q+4

p+4:q+4=2:3
p+4/q+4=2/3

p=54-q, put in p+4/q+4=2/3

54-q+4/q+4=2/3
58-q/q+4=2/3
(58-q)3=(q+4)2
174-3q=2q+8
-3q-2q=-174+8
-5q=-166
q=32.2

put the value of q in p=54-q

p=54-32.2
p=21.8

Answer 2

Answer:

The required present age $p$ is $21.8$

Step-by-step explanation:

Concept:

Age problems are an example of a situation where linear equations are used. When resolving age-related issues, two separate individuals (or things') ages from the present to the past or future are typically compared. Typically, the goal of these puzzles is to determine the present age of each subject.

Given:

The sum of present ages of p and q is $54$ years

The ratio of their ages will be $2:3$

To find:

The objective is to find out the present age of p.

Solution:

$p+q=54\\p=54-q$

After $4$ years,

$P=p+4\\Q=q+4$

Then,

$p+4:q+4=2:3$

⇒$\frac{p+4}{q+4} =\frac{2}{3}$

Put $p=54-q$ into the $\frac{p+4}{q+4} =\frac{2}{3}$

$\frac{54-q+4}{q+4} =\frac{2}{3}$

⇒$\frac{58-q}{q+4} =\frac{2}{3}$

⇒$(58-q)3=(q+4)2$

⇒$174-3q=2q+8$

⇒$-5q=-166$

⇒$q=32.2$

Put the value of $q$ in $p=54-q$

$p=54-32.2\\p=21.8$

Therefore, the present age $p$ is $21.8$.

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