Question

The ratio of the present ages of Mohan and Sohan
is 5: 4. Sixteen years hence, the ratio of the ages
of Mohan and Sohan will be 7:6. Find the present
age of Mohan.
(1) 45 years
(2) 35 years
(3) 50 years
(4) 40 years​

Answer 1

Step-by-step explanation:

Let x be the present age of mohan and sohan then present age of mohan is 5x and that of sohan is 7x. 

According to 1st condition -

Mohan's age will be 5x+9

Sohan's age will be 7x−9

⇒5x+9:7x−9=2:1

⇒7x−95x+9=12

⇒(5x+9)=2(7x−9)

⇒5x+9=14x−18

⇒5x−14x=−18−9

⇒−9x=−27

⇒x=3

Present age of mohan is 5x=5×3=15

Present age of sohan is 7x=7×3=21

hence, solved. 

Answer 2

Given :-

Given that the ratio of the present ages of Mohan and Sohan is 5:4. Sixteen years, the ratio will be 7:6.

To find :-

We have to find their present age of Mohan.

Solution :-

Let the ages of

• Mohan be x.
• Sohan be y.

According to the question :

»» x/y = 5/4

Cross multiplying :

»» 4x = 5y

»» x = 5y/4 ....[1]

After 16 years :

»» (x+16)/(y+16) = 7/6

Cross multiplying :

»» 6(x+16) = 7(y+16)

»» 6x + 96 = 7y + 112 ....[2]

Substituting [1] in [2] and solving :

»» 6(5y/4) + 96 = 7y + 112

»» 15y/2 + 96 = 7y + 112

»» 15y/2 - 7y + 96 - 112 = 0

»» (15y - 14y)/2 - 16 = 0

»» y/2 - 16 = 0

»» y/2 = 16

»» y = 32

Substituting y=2 in [1] :

»» 5(32)/4 = x

»» 160/4 = x

»» x = 40

____________________

Therefore, Mohan's age (x) is 40 years (Option 4).