i) Let the breadth be x m and the length will be 2x+1 m.Area =l×bArea =x(2x+1)=5282x2+x−528=02x2+33x−32x−528=0⇒2x(x−16)+33(x−16)=0⇒(2x+33)(x−16)=0⇒x=16,233​Breadth =16 m and length =33 mii) Let one number be x then the next number will be x+1x(x+1)=306⇒x2+x−306=0⇒x2+18x−17x−306=0⇒x(x+18)−17(x+18)=0⇒(x+18)(x−17)=0⇒x=17,−18The numbers are 17 and 18.iii) Let Rohan's present age =x yrs.Then his mother's present age =x+26 yrsAfter 3 yrs Rohan's age =x+3 yrsHis mother's age =x+29 yrs(x+3)(x+29)=360⇒x2+32x+87−360=0⇒x2+32x−273=0⇒x2+39x−7x−273=0⇒x(x+39)−7(x+39)=0⇒(x+39)(x−7)=0⇒x=7,−39So, Rohan's present age =7 yrs.iv) Let the speed of the train =x km/hr(x−8)480​−x480​=3⇒480x−480x+3840=3x(x−8)⇒3x2−24x−3840=0⇒x2−8x−1280=0⇒x2−40x+32x−1280=0⇒x(x−40)+32(x−40)=0⇒(x+32)(x−40)=0⇒x=40,−32The speed of the train is 40 km/hr.