Question

the age of sumit and sunita are in ratio of 3:4 before four year their age were in ratio 5:7 find their present age​

Answer 1

Answer:

Sumit age = 24, Sunita age = 32

Answer 2

Answer :

$\underline{\boxed{\sf{\bold{Present\:age\:of\:Sumit\:is\:24\:years}}}}$

$\underline{\boxed{\sf{\bold{Present\:age\:of\:Sunita\:is\:32\:years}}}}$

Step-by-step explanation :

The age of sumit and sunita are in ratio of 3:4

Let the present age of Sumit be 3M and Sunita be 4M years.

Before four years, their age were in ratio 5:7.

• Age of Sumit = (3M - 4) years
• Age of Sunita = (4M - 4) years

According to question,

$\implies\:\sf{\dfrac{3M-4}{4M-4}\:=\:\dfrac{5}{7}}$

Cross-multiply them,

$\implies\:\sf{7(3M-4)\:=\:5(4M-4)}$

$\implies\:\sf{21M\:-\:28\:=\:20M\:-\:20}$

$\implies\:\sf{21M\:-\:20M\:=\:28\:-\:20}$

$\implies\:\sf{\boxed{M\:=\:8}}$

Therefore,

Present age of Sumit = 3M

$\Rightarrow\:\sf{3(8)}$

$\Rightarrow\:\sf{24\:years}$

Present age of Sumita = 4M

$\Rightarrow\:\sf{4(8)}$

$\Rightarrow\:\sf{32\:years}$

Verification :

From above we have M = 8

Substitute value of M in $\sf{\dfrac{3M-4}{4M-4}\:=\:\dfrac{5}{7}}$

$\rightarrow\:\sf{\dfrac{3(8)-4}{4(8)-4}\:=\:\dfrac{5}{7}}$

$\rightarrow\:\sf{\dfrac{24-4}{32-4}\:=\:\dfrac{5}{7}}$

$\rightarrow\:\sf{\dfrac{20}{28}\:=\:\dfrac{5}{7}}$

$\rightarrow\:\sf{\dfrac{5}{7}\:=\:\dfrac{5}{7}}$