Question

The present ages of Rohan and Sohan are in the ratio 4:5. Four years hence (from now) their ages will be in the ratio 5 : 6. Find their present ages.
$= > no \: spam$
​

Answer 1

Answer:

Let the age of Rohan be 4x and that of Sohan be 5x

Therefore, four years from now,their age will be :-

Rohan=4x+4 and Sohan = 5x+4

According to the question,

(4x+4)/(5x+4)=5/6

Multiplying both the sides with 5x+4

5x+4(4x+4)/(5x+4)=5(5x+4)/6

(4x+4)=5(5x+4)/6

Multiplying both the sides with 6

6(4x+4)=6*5(5x+4)/6

6(4x+4)=5(5x+4)

24x+24=25x+20

Subtracting 20 from both the sides

24x+24-20=25x+20-20

24x+4=25x

Subtracting 24x from both the sides

24x+4-24x=25x-24x

4=x

x=4

So,age of Rohan is 4x=4*4=16 years And age of Sohan is 5x=5*4=20 years

Verifications:

According to the question,

(4x+4)/(5x+4)=5/6

(4*4+4)/(5*4+4)=5/6

(16+4)/(20+4)=5/6

20/24=5/6

(4*5)/(4*6)=5/6

5/6=5/6

Since LHS=RHS

Hence verified that x=4 and ages of Rohan and Sohan are 16 and 20 respectively..

Step-by-step explanation:

Well, hope it helps you...

Your welcome in advance..

(◍•ᴗ•◍)

Answer 2

Answer:

Rohan's age = 16 years

Sohan's age = 20 years

Step-by-step explanation:

Present Age:

Rohan's age : Sohan's age = 4 : 5

Rohan's age = 4x

Sohan's age = 5x

After 4 years:

Rohan's age = 4x + 4

Sohan's age = 5x + 4

Now their ratio of age = 5 : 6

4x +4 : 5x + 4 = 5 :6

$\dfrac{4x+4}{5x+4}=\dfrac{5}{6}$

Cross multiply

6*(4x + 4) = 5*(5x+4)

6*4x + 6*4 = 5*5x + 5*4

24x + 24 =25x + 20

Subtract 20 from both sides

24x + 24 - 20 = 25x

24x + 4 = 25x

Subtract 24x from both sides

4 = 25x - 24x

4 = x

x = 4

Rohan's age = 4x = 4*4 = 16 years

Sohan's age = 5x = 5*4 = 20 years