There are three earning members in a family - Mr Roy, Mrs Roy and their daughter Teena. the average monthly income of Mr and Mrs Roy is 5050., whereas the average monthly income of Mrs Roy and Teena is 6250. The average monthly income of Mr Roy and Teena is 5200. What is Mr Roy's income ( with full steps )

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2014-11-07T14:12:22+05:30
There are three earning members in a family - Mr Roy, Mrs Roy and their daughter Teena. the average monthly income of Mr and Mrs Roy is 5050., whereas the average monthly income of Mrs Roy and Teena is 6250. The average monthly income of Mr Roy and Teena is 5200. What is Mr Roy's income ( with full steps )

solution :
       Let the monthly income of Mr Roy(in Rupees) = x
       Let the monthly income of Mrs Roy(in Rupees) = y
       Let the monthly income of Teena (in Rupees)= z
       according to question ,
           x+y/2 = 5050
         or x+y =5050*2
         or x+y =10100.............. (1st)
          

the average monthly income of Mrs Roy and Teena is 6250
           y+z / 2 = 6250
           y+z=2*6250
           y+z=12500----------------------(2nd)

average monthly income of Mr Roy and Teena is 5200.
                   x+z /2= 5200
                   x+z= 2*5200
                   x+z =10400--------------------(3rd)
subtract 3rd from 1st , we get
               x+y - (x+z)=10100 - 10400
               x+y -x -z = -300
                 y-z = -300
                 or y= z- 300
  substitute y = z - 300 in equation 2nd , we get
               z- 300 + z = 12500
               2z =12500+300
               2z = 12800
               or z = 12800/2
                   z= 6400
Hence Teena's monthly income is rupees 6400.
  Substitute z= 6400 in 3rd equation ,
                   x+z=10400
                   x+6400 =10400
                   x=10400 -6400
                   x=4000
Therefore , Mr Roys monthly income is Rs 4000

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3 5 3
2014-11-07T18:53:31+05:30
the avg of Mr Roy and Mrs Roy=5050⇒ (Mr R+Mrs R)/2=5050
                                                                   ⇒ Mr R+Mrs R=10100.......(I)
the avg of Mr Roy and Teena=5200⇒(Mr R+T)/2=5200
                                                                ⇒Mr R+T=10400.......(II)
the avg of Mrs Roy and Teena =6250⇒(Mrs R+T)/2=6250
                                                                   ⇒Mrs R+T=12500..........(III)

Adding all the eqns we get
2(Mr R+Mrs R+T)=33000
Mr R+Mrs R+T=16500.....(IV)

now subtracting (III) from (IV)
we get,
Mr Roy =total earning -(
Mrs R+T)
⇒Mr Roy's earning=16500-12500=4000





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