Math Soultion-3

Hello, guys here is the set of solutions ,to yesterday's questions 

1) let the present ages of mther and daughter  be M and D
    M-5=4(D-5)  =>(1)
    M+15=2(D+15) => (2)

  solving (1) and (2) ,we get
 D= 15 years

2) Portion of work completed in 4 days = 4*1/8 = 1/2

   Portion of work to be completed in next 4 days

   = 4*1/12 = 1/3

   portion of work to be completed =

   = 1-(1/2+ 1/3)
  
   = 1/6

   Portion of work that B and C can complete in 1 day = 1/12 + 1/24 = 1/8
   Time taken to do 1/6 work by B and C  = (1/6)/(1/8)
      =  4/3 days
 Time taken to complete the entire work is ( 4 + 4 + 4/3 ) days
           = 9.33 days

3) equations is 8x^2 -22x +15 =0
   roots are given by
   (-b + root of (b^2 - 4*a*c))/2*a and (-b - root of (b^2 - 4*a*c))/2*a

   hence from the above equations roots are
   (22 + root of (484 -480 ))/16 and   (22 - root of (484 -480 ))/16
   => roots are 3/2 ,5/4
    LCM (3/2 ,5/4) = LCM(3,5)/HCF(2,4) = 15/2
    HCF(3/2 ,5/4) = HCF(3,5) /LCM(2,4) =1/4
   => LCM:HCF = (15/2)/(1/4) = 30:1

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