Question

One year ago ratio of age of Rohit and Sahil was 6: 7, their ratio four years from
now will be 7: 8. How old is Sahil?​

Answer 1

Answer:  The present age of Sahil is 36 years.

Step-by-step explanation:  Given that one year ago, the ratio of age of Rohit and Sahil was 6: 7 and the ratio four years from  now will be 7: 8.

We are to find the present age of Sahil.

Let x years and y years represents the present ages of Rohit and Sahil respectively.

According to the given information, we have

$\dfrac{x-1}{y-1}=\dfrac{6}{7}\\\\\\\Rightarrow 7(x-1)=6(y-1)\\\\\Rightarrow 7x=6y-6+7\\\\\Rightarrow 7x=6y+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$\dfrac{x+4}{y+4}=\dfrac{7}{8}\\\\\\\Rightarrow 8(x+4)=7(y+4)\\\\\Rightarrow 8x+32=7y+28\\\\\Rightarrow 8x=7y-4\\\\\\\Rightarrow 8\times\dfrac{6y+1}{7}=7y-4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\\Rightarrow 48y+8=49y-28\\\\\Rightarrow 49y-48y=8+28\\\\\Rightarrow y=36.$

Thus, the present age of Sahil is 36 years.