Question

the ratio of present ages of Albert and Salim is 5:9. five years hence ratio of their ages will be 3:5. find their present ages?​

Answer 1

Answer:

Step-by-step explanation:

Given :-

The ratio of present ages of Albert and Salim is 5 : 9.

Five years hence ratio of their ages will be 3 : 5.

To Find :-

Their Present Ages

Solution :-

Let present age of Albert be 5x years.

And present age of Salim be 9x years.

Five years later,

Five years later, age of Albert = (5x + 5) years

Five years later, age of Salim = (9x + 5) years

According to the Question,

⇒ 5x + 5/9x + 5 = 3/5

⇒ 25x + 25 = 27x + 15

⇒ 27x – 25x = 25 – 15

⇒ 2x = 10

⇒ x = 10/2

⇒ x = 5

Present age of Albert = 5x = 5 × 5 = 25 years

Present age of Salim = 9x = 9 × 5 = 45 years

Answer 2

$\bold{\underline{\underline{\huge{\tt{AnsWer:}}}}}$

Present age of Albert = 25 years

Present age of Salim = 45 years

$\bold{\underline{\underline{\large{\tt{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• The ratio of present ages of Albert and Salim is 5:9.
• Five years hence ratio of their ages will be 3:5.

To FiNd :

• Present age of Albert
• Present age of Salim

SoLuTiOn :

Let x be the common multiple of the ratio 5:9.

Present age of Albert = 5x

Present age of Salim = 9x

$\bold{\sf{\underline{\underline{As\:per\:the\:question:}}}}$

• Five years hence ratio of their ages will be 3:5

Ages 5 years hence :

Albert's age = 5x + 5 years

Salim's age = 9x + 5 years

Ratio = 3:5

Constituting it mathematically,

$\longrightarrow$$\bold{\sf{\dfrac{5x-5}{9x+5}}}$ = $\bold{\sf{\dfrac{3}{5}}}$

Cross multiplying,

$\longrightarrow$$\bold{\sf{5(5x+5)\:=\:3(9x+5)}}$

$\longrightarrow$$\bold{\sf{25x+25\:=\:27x\:+\:15}}$

$\longrightarrow$$\bold{\sf{25x-27x=15-25}}$

$\longrightarrow$$\bold{\sf{-2x=-10}}$

$\longrightarrow$$\bold{\sf{x\:=\:{\dfrac{-10}{-2}}}}$

$\longrightarrow$$\bold{\sf{x\:=\:{\dfrac{10}{2}}}}$

$\longrightarrow$$\bold{\sf{x=5}}$

Substitute x = 5 in the ratio of present ages,

$\bold{\large{\boxed{\rm{\red{Present\:age\:of\:Albert\:=\:5x\:=\:5\:\times\:5\:=\:25}}}}}$

$\bold{\large{\boxed{\rm{\red{Present\:age\:of\:Salim\:=\:9x\:=\:9\:\times\:5\:=\:45}}}}}$