Question

the ages of simmy and Jimmy are in the ratio 6:8 five years from now the ratio of their ages will be 4:5 find their present ages​

Answer 1

⇒ Given:

Current ages of Simmy and Jimmy are in the ratio 6:8.

Five years later, their ages are in the ratio 4:5.

⇒ To Find:

Their current ages.

⇒ Solution:

It is given that the current ages of Simmy and Jimmy are in the ratio 6:8. Assuming the ages as 6x and 8x,

It can be represented in fractional form as:

$\sf{\implies\:6:8=\dfrac{6x}{8x}}$

So, five years from now, their ages are 6x + 5 and 8x + 5 respectively.

It is given that, 5 years later, their ages are in the ratio 4 : 5.

Writing the given statements in equational form:

$\sf{\implies\dfrac{6x+5}{8x+5}=\dfrac{4}{5}}$

Doing cross multiplication:

$\sf{\implies5(6x+5)=4(8x+5)}$

Opening the brackets:

$\sf{\implies30x+25=32x+20}$

Grouping the constants and variables:

$\sf{\implies30x-32x=20-25}$

$\sf{\implies-2x=-5}$

$\sf{\implies\:x=\dfrac{5}{2}}$

The value of x is 5/2.

So,

$\sf{\maltese\:Simmy=6x=6\times\dfrac{5}{2}}$

$\sf{=3\times5}$

$\bf{=15\:years\:old.}$

$\sf{\maltese\:Jimmy=8x=8\times\dfrac{5}{2}}$

$\sf{=4\times5}$

$\bf{20\:years\:old.}$

Therefore the ages of Simmy and Jimmy are 15 and 20 years respectively.