 Hello and welcome to the session. In this session we discussed the following question which says the ages of Sohan and Mohan are in the ratio 7 is to 5, 10 years hence the ratio of the ages will be 9 is to 7, find their present ages. Let's move on to the solution now. We are given that the ratio of the ages of Sohan and Mohan is 7 is to 5 so we have age of Sohan upon age of Mohan would be equal to 7 upon 5. Now we take let the present age of Sohan be equal to x years so we get the present age of Mohan equal to 5x upon 7 years that is in this we put the age of Sohan as x and we get the age of Mohan or the present age of Mohan as 5x upon 7 years. Now after 10 years age of Sohan would be equal to x plus 10 years and age of Mohan would be equal to 5x upon 7 plus 10 years. Now according to the question we have that 10 years after the ratio of the ages will be 9 is to 7 so we have x plus 10 is to 5x upon 7 plus 10 is equal to 9 is to 7 or we can say that x plus 10 upon 5x upon 7 plus 10 is equal to 9 upon 7 this gives us x plus 10 upon 5x plus 70 upon 7 is equal to 9 upon 7. We have taken the LCM in the denominator this gives us 7 into x plus 10 upon 5x plus 70 is equal to 9 upon 7 that is we have 7x plus 70 upon 5x plus 70 is equal to 9 upon 7. Now cross multiplying we get 7 into 7x plus 70 is equal to 9 into 5x plus 70. Now we open the brackets on both the sides so we get 49x plus 490 is equal to 45x plus 630. Now we transpose this term 45x from right hand side to the left hand side and we transpose this constant term 490 from the left hand side to the right hand side. So we get 49x minus 45x is equal to 630 minus 490. This gives us 4x is equal to 140 that is we get x is equal to 140 upon 4 then 4 35 times is 140 that is we get x is equal to 35. We had assumed the present age of Sohan to be x years so we now say that the present age of Sohan is equal to 35 years and the present age of Mohan is equal to 5x upon 7 years and we put the value for x as 35 in this so we get 5 into 35 upon 7 years. Now 7 5 times is 35 so this is equal to 25 years so we get the present age of Sohan as 35 years and present age of Mohan as 25 years. So with this we complete the session hope you have enjoyed the session.