Question

The present ages of the eldest and youngest managers in an organization are in the ratio of 2:3 if after 8years the ratio of their ages becomes 5:7, then what is the age of the youngest manager in that organization?
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Answer 1

Given:

The present ages of the eldest and youngest managers in an organization are in the ratio of 2:3 if after 8years the ratio of their ages becomes 5:7

To find:

What is the age of the youngest manager in that organization?

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Solution:

The ratio of present ages of the eldest and youngest managers = 2:3

So, let

"2x" → the present age of the eldest managers

"3x" → the present age of the youngest managers

After 8 years:

The age of eldest managers = 2x + 8

The age of youngest managers = 3x + 8

The new ratio of their ages after 8 years becomes = 5 : 7

Now, we get the final equation as:

$\frac{2x\: +\: 8}{3x\:+\:8} = \frac{5}{7}$

$\implies 7(2x\: +\: 8) = 5(3x\:+\:8)$

$\implies 14x\: +\: 56 = 15x\:+\:40$

$\implies 15x \:-\:14x\: = \: 56 \:-\:40$

$\implies x\: = \: 16$

∴ The age of the youngest manager = $3x = 3 \times 16 = 48\:years$

Thus, the age of the youngest manager in that organization is → 48 years.

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