Represent the following situations in the form of quadratic equations: (iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age. (ii) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken

(iii) Let us consider,

Age of Rohan’s = x  years

Therefore, as per the given question,

Rohan’s mother’s age = x + 26

After 3 years,

Age of Rohan’s = x + 3

Age of Rohan’s mother will be = x + 26 + 3 = x + 29

The product of their ages after 3 years will be equal to 360, such that

Therefore, the age of Rohan and his mother, satisfies the quadratic equation, , which is the required representation of the problem mathematically.

(iv) Let us consider,

The speed of train = x  km/h

And

Time taken to travel 480 km = 480/x km/hr

As per second condition, the speed of train = (x – 8) km/h

Also given, the train will take 3 hours to cover the same distance.

Therefore, time taken to travel 480 km

As we know,

Therefore,

Therefore, the speed of the train, satisfies the quadratic equation, , which is the required representation of the problem mathematically.