Question

The ratio of the present ages of m and n are 2:3. If the ratio of their ages after 5 years becomes 3:4, then the present ages of m and n are ________ and _______,
respectively.​

Answer 1

Answer:

m = 10 years and n = 15 years

Step-by-step explanation:

Given that the ratio of the present ages of m and n are 2:3. If the ratio of their ages after 5 years becomes 3:4.

We need to find out the present ages of m and n.

Let's say the present age of m is 2a years and of n is 3a years.

After 5 years,

• Age of m = (2a + 5) years
• Age of n = (3a + 5) years

As per question,

→ (2a + 5)/(3a + 5) = 3/4

Cross multiply them,

→ 4(2a + 5) = 3(3a + 5)

→ 8a + 20 = 9a + 15

→ 9a - 8a = 20 - 15

→ a = 5

Hence, the present age of m is 10 years (2*5) and of n is 15 years (3*5).

Answer 2

Given,

The ratio of the present ages of $m$ and $n$ are $2:3$. If the ratio of their ages after $5$ years becomes $3:4$.

Let present ages of $m$ and $n$ be $2x$ and $3x$.

After $5$ years their ages

$m$ age after $5$ years $= 2x+5$

$n$ age after $5$ years $= 3x+5$

The ratio of their ages after $5$ years becomes $3:4$

Now, we can find the present ages

$\frac{2x+5}{3x+5}=\frac{3}{4}$

$4(2x+5)=3(3x+5)$

$8x+20=9x+15$

$9x-8x=20-15$

$x=5$

Substitute $x= 5$ in present ages $m$ and $n$

$m=$$2x=2\times5=10$years

$n=3x=3\times5=15$ years

Therefore, the present ages of  $m$ and $n$ is $10$ and $15$ years.