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1 Downloded From: UNIT-3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES Like the crest of pecock so is mthemtics t the hed of ll knowledge.. At certin time in deer prk, the numer of heds nd the numer of legs of deer nd humn visitors were counted nd it ws found there were 39 heds & 3 legs. Find the numer of deer nd humn visitors in the prk. (Ans:7,) Ans: Let the no. of deers e And no. of humns e ASQ : + = () 4 + = () Multipl () nd () On solving, we get = 7 nd = No. of deers = 7 nd No. of humns =. Solve for,. 8 = 3 4 = 3 (Ans: =, =6) Ans: + 8 = + 4 = =

2 Downloded From: On solving, we will get.= = - = On solving, we will get. =. 7( + 3) ( + ) = 4, 4 ( ) + 3( 3) = Ans: 7( + 3) (+ ) = () 4( ) + 3( 3) = () From () = 4 On solving, we will get. 7 3 = (3) From () = On solving, we will get = (4) Sustitute this, to get = nd = 5 = 5 nd = c. (+) + ( ) =, ( ) + ( +) = 3 (Ans: 5 0, 0 0 ) Ans: + 4 =, we get 4 = = 5 4 = - Solve this, to get = Similrl, we cn solve for 4

3 Downloded From: Ans: d. + = +, = + + = ; 0, 0 (Ans: =,=B ) = = + = On solving, we get = nd = e. + 3 = 7, = 5 Ans: + 3 = 7, = 5 Let e nd 3 e + 3 = 7 + = () = = () on solving, we get.. = 8 from () + = - 7 = 9, = 8 = 3, = 5

4 Downloded From: f. If = 3 4, Find Ans: On dividing, we get 5 8 g = 35, =47 Ans: = 35, = 47 Add the two equtions : Solve it, to get + = () Sutrct : Solve it, to get,. = () From () nd () + = 3 = on solving, we get = nd = 3. Find the vlue of p nd q for which the sstem of equtions represent coincident lines +3 = 7, (p+q+) +(p+q+) = 4(p+q)+ Ans: =, = 3, c = 7 = p + q +, = p + q +, c = (p + q )+ For the following sstem of eqution the condition must e c c => p q p 3 q 4( p 7 q) => p q 4( p 7 q) 7p +4q + 4 = p + q + 3 6

5 Downloded From: = 5p - q - = () p + q = 0 5p - q - = 0 From () nd () 5p + 5q - 5 = 0 5p - q - = 0 Solve it, to get q = Sustitute vlue of q in eqution () p + q - 5 = 0 On solving we get, p = 3 nd q = 4. Students re mde to stnd in rows. If one student is etr in row there would e rows less. If one student is less in row there would e 3 rows more. Find the numer of students in the clss. Ans: No. of rows e Let the numer of students e Numer of students in the clss will e = One student etr, rows less ( + ) ( ) = + - = -(- + -) = 0 + = () One student less, three more rows ( - ) ( + 3) = = 3 - = () From () & () = - X = 3 X - Solve it, to get = nd = 5 Numer of student = = X 5 = 60 students 7

6 Downloded From: 5. The lrger of two supplementr ngles eceeds the smller 8 0, find them. (Ans:99 0,8 0 ) Ans: + = 80 0 = = 98 = 98 / = = = 80 0 = = A trin covered certin distnce t uniform speed. If the trin would hve een 6km/hr fster, it would hve tken 4hours less thn the scheduled time. And if the trin were slower 6km/hr, it would hve tken 6 hours more thn the scheduled time. Find the distnce of the journe. Ans: Let the speed of the trin km/hr And the time tken it Now distnce trveled it is = APQ: I--- ( + 6) ( - 4) = 4 6 = -4 => 3 = () II--- ( - 6) (+ 6) = 6 6= 36 => = () Solving for nd we get = 4, = 30 So the distnce =30 4 = 70 km 7. A chemist hs one solution which is 50% cid nd second which is 5% cid. How much of ech should e mied to mke 0 litres of 40% cid solution. (Ans:6L,4L) Ans: Let 50 % cids in the solution e Let 5 % of other solution e Totl Volume in the miture = + 8

7 Downloded From: A.P.Q: + = () 50 5 A.P.Q: = () = So = 6 & = 4 8. The length of the sides of tringle re +, 3 tringle is equilterl. Find its perimeter. Ans: + = () = () nd If the = (3) 6 APQ: 4+ = = = = (4) 4 + = = Solve it, To get 8 9 = (5) Solve it, To get = 3 Sustitute vlue of in (4) 3 = 3 9

8 Downloded From: Solve it, To get = So the vlues of = 3 nd = + = 6.5 cm Perimeter = 6.5 cm cm cm Perimeter = 9. 5cm the perimeter of the tringle is 9.5 cm 8. In n election contested etween A nd B, A otined votes equl to twice the no. of persons on the electorl roll who did not cst their votes & this lter numer ws equl to twice his mjorit over B. If there were 8000 persons on the electorl roll. How mn voted for B. Ans: Let nd e the no. of votes for A & B respectivel. APQ: The no. of persons who did not vote = (8000 ) = (8000 ) => 3 + = () & (8000 ) = () ( ) => 3 = () On solving we get, = 6000 nd = 8000 Vote for B = When 6 os were dmitted & 6 girls left the percentge of os incresed from 60% to 75%. Find the originl no. of os nd girls in the clss. Ans: Let the no. of Bos e Girls e APQ: Totl = + 0

9 Downloded From: () 6 75 ( 6)( 6) 00 On solving we get, = 4 nd = When the son will e s old s the fther tod their ges will dd up to 6 ers. When the fther ws old s the son is tod, their ges dd upto 38 ers. Find their present ges. Ans: let the son s present ge e Fther s ge e Difference in ge ( ) Of this difference is dded to the present ge of son, then son will e s old s the fther now nd t tht time, the fther s ge will e [ + ( )] APQ: [ + ( )] + [ ( )] = 6 [ + ( )] + [ + ( )] = 38 Solving we get the vlue of nd. A cclist, fter riding certin distnce, stopped for hlf n hour to repir his iccle, fter which he completes the whole journe of 30km t hlf speed in 5 hours. If the rekdown hd occurred 0km frther off, he would hve done the whole journe in 4 hours. Find where the rekdown occurred nd his originl speed. (Ans: 0km, 0km/hr) Ans: Let e the plce where rekdown occurred e the originl speed ( 0 ) 4

10 Downloded From: On solving, we get, = 0 km nd = 0 km/h. The popultion of the villge is If in er, the numer of mles were to increse 5% nd tht of femle 3% nnull, the popultion would grow to 50 t the end of the er. Find the numer of mles nd femles in the villge. Let the numer of Mles e nd femles e Ans: + = = = 000 On solving & we get = 600 =400 No. of mles = 600 No. of femles = 400

UNIT-4. File downloaded from For the things of this world cannot be made known without a knowledge of mathematics.

UNIT-4. File downloaded from For the things of this world cannot be made known without a knowledge of mathematics. File downloded from http://jsuniltutoril.weely.com UNIT- For the things of this world cnnot e mde known without knowledge of mthemtics.. Solve y fctoriztion. - + ( ) = 0 Ans: + ( - ) = 0. [( + ) + ( -