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. The time Exavelled by the ball, = 3.75 seconts-, %3D, Example : 3.36. The product o, buwo years ago and his age four years from, f e, KUmaran's, age, Cin years)., now is, one, more than twice his present age. What is his present oge?, Soln:, Let the, present, age of, Kumaran be x years., Two years ago,, = x-2 years, Kumaran's, age, Four, years from now,, his age = x+4 years., Given :, (x - 2) (x+4), = I +22e, x-2x+4x- 8, =(+ 2x, X+2x-8-1-2C, x²-9, x²=9, %3D, x =+9., %3D, x = -9 (not possible), is 3 years., 17 feet long is leaning ogainst a, .: Kumaran's present age, Example : 337 :, A ladder, the, coall. If the ladder, vertical wall aned the floor from, bottom of the wall bo the ladder form a right briangle, find Ehe, height d the wwall where the bop of the ladder meets if, the distance bebween bobbom of the coal! to botbom of, the ladder is 7 feet less than the height of Ehe wall?, Soln:, bet the height of the wall = x feet, Given :, MN =x -7) feet., feet, In right ALMN,, LMTMN=LN², x²4 (x-7)"=(17), x²+x=14X +49 = 289, 29c?- 14X, = 284-49, x²-7X, 240, %3D, =120, 2., x- 7x -120 =0, be²+8) (x-15) = o

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x+8=0, X-15 =0, X =-8, 2 =15, not possible., -. The height of the wall, = 15 feet., Example: 3-38. A Hock of swans contained x members., As Bhe clouds gathered tox went to a lake and one-, * the members Haw, pairs played, in total?, Soln:, Given : There, to a garden. The remaining Eree, away, about in the water. How, many, Swans WEYE there, are x Swans., x10x-c² =6 ., 8x-80x -x? =48, -336, 7x-80x -48 =0, - 84 4, 80, - 84, (oc-12) (x +$) -0, x+속-0, x = -4, X-12=0, 4 not passible., X=12, Total no-, swans =x²-12, of, A passenger train takes Thy more, 144., Example : 3:39, an express train to travel a distance of 240 km from, chennai to Virudhachalam. The speed of passenger Erain, is less than Ehat of, than, an express Evain by 2olomper hour., Find the average speed of both the trains., Soln:, Let the average, spead of passeger brain = x km/h., Erain = x+20 km r, Then the average speed of exxpress, Time =, Distance, Speed., Time Ealken, by passenger, Erain, =240 hr.

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Time taken by express Erain, 240, X+20, Given:, 240, 240, +1, 父十20, 240, 240, X+20, 240, = 1, X+20, 240, X+20, -4800, 240 (20), - x (x+20), 4 800, = x+20e, 80 -60, x+20x -4800 = 0, 20, (x+80)(x -60) - -, x+ 80 =0, x-60 =e, 80, X = 60., Not possible., train, 60 km/hr, . Avevage speed of, Average speed of the, the, %3D, passenger, Erain, express, = 80 km /hr., Exercise :3.12., 1-It the diflerence, reciptocal is 24, 80ln;, Lek the number be x., between a number and its, tind the number., 24, Given:, = 24, 5x 5, = 24X, 5x-24x-5=0

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pedestrain pathoay that is 'w' meters wide, installed all the way around 80 that it increases, (x*-5) (6x -1) =0, -25, X-5=0, -25, 5x+1=0, -24, garden measuring 12m by lbm is bo have a, the pathway?, 8oln:, Length -(16+2w ) m, Breadth =(12+2w) m, 12m, 1272w, 16m, Area, - 286 m, 16+2w, Area, uniti ., (1642w) (12+2w), =285, 4x698)=, -372, Aw +2Aw+320+192 =285, 62 -6, 4w456w +192-285 =0, 56, Aw+56w -, 9 3, w =-3), Not passible, .. The width of the pathway = 1-5m,, 2, W=1.5m, %3D, 3. A bus covers a distance of 90 km ab a uniform speed., Had the speed been 15 km/hour mode it would have, baken 30 minutes less tor the, journey., Find the, original speed of the bus?, Soln:, Let the original speed of the bus = x konyhor.

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Distance - 9okm., Time, 90, If speed increases by 15 km /hr,, Time elecrea, ses by 30 minubes =, 90, 90, x+5, 90/ 2x+5-x, Oc+5) (x), (x -x+*), 180, X +5, x (x+5), -900, %3D, | 80 (+ 5), 50, -45, x²+5x, %3D, +-52 -१०० = ০, (sc + 50) x-45), X+50=O, X-45 =O, X = - 50, X = 45, Not possible, - The original epeed of the bus = 45 km/hr., 4. A girl is twice as old as her sister. Five yeaYs hence,, the prod vet of, their present ages., their, ages, Cin yrs) will be 375., Find, Soln:, Let the Girls present age be x., Then Siste's present age, %3D, 2x., After 5 yeays, PRroduct their, of, oges, = 375, 2x(-350)= -700, (x+5) (2x +5) =375, -20 35, 20+ 5X+HOX +25-375=0, 2x+15x-350, (x-10) (x+35, 2., -10, X 10 =0, X =10, x =-35 (not possible)., :. Girks present age = 10, 2., Sister's present age = 20.