Question

The ages of arun and akash are in the ratio of 7:5 after 6 years, their ages would be in the ratio of 5:4 .find their present ages. ​

Answer 1

Let present age of Arun be 7M and present age of Akash be 5M.

After 6 years, their ages would be in the ratio 5:4.

After 6 years,

• Age of Arun = (7M + 6) years
• Age of Akash = (5M + 6) yeas

According to question,

$\implies\:\dfrac{7M\:+\:6}{5M\:+\:6}\:=\:\dfrac{5}{4}$

$\implies\:4(7M\:+\:6)\:=\:5(5M\:+\:6)$

$\implies \:28M\:+\:24\:=\:25M\:+\:30$

$\implies\:28M\:-\:25M\:=\:24\:-\:30$

$\implies\:3M\:=\:6$

$\implies\:\bold{M\:=\:2}$

∴ Present age of Arun = 7M

=> $\sf{7(2)}$

=> $\sf{14\:years}$

∴ Present age of Akash = 4M

=> $\sf{5(2)}$

=> $\sf{10\:years}$

Answer :-

•°• $\sf{\underline {Present \:age\:of\:Arun\:is\:14\:years\:and}}$ $\sf{\underline {Present \:age\:of\:Akash\:is\:10\:years}}$

Answer 2

$\huge\underline\blue{\sf Answer:}$

$\large\red{\boxed{\sf Present\:age\:of\:Arun=14years}}$

$\large\red{\boxed{\sf Present\:age\:of\:Aakash=10years}}$

$\huge\underline\blue{\sf Solution:}$

$\large\underline\pink{\sf Given: }$

• Ratio of ages of Arun:Akash =7:5

• After 6 years their ages ratio = 5:4

$\large\underline\pink{\sf To\:Find: }$

• Present age of Arun and Akash = ?

━━━━━━━━━━━━━━━━━━━━━━━━━━

Let ,

Present age of Arun = 7X

and Present age of Akash = 5X

After 6 years their ages would be in ratio 5:4

After 6 years :

Age of Arun = (7X + 6) years

Age of Akash = (5X + 6) years

According to questions :

$\large{\sf{\frac{7X+6}{5X+6}}={\frac{5}{4}}}$

$\large\implies{\sf 4(7X+6)=5(5X+6)}$

$\large\implies{\sf 28X-25X=24-30}$

$\large\implies{\sf 3X=6 }$

$\large\implies{\sf X=2 }$

Therefore ,

On putting value of X :

Present age of Arun = 7 X

$\large\implies{\sf 7×2}$

$\large\implies{\sf 14 years }$

$\huge\red{♡}$$\large\red{\boxed{\sf Present\:Age\:of\:Arun=14\: years}}$

Present age of Akash = 5X

$\large\implies{\sf 5×2}$

$\large\implies{\sf 10\:years }$

$\huge\red{♡}$$\large\red{\boxed{\sf Present\:Age\:of\:Akash=10\:years}}$