Question

raj takes a certain number of rotis during lunch but always wastes half a roti.riya takes half the number of rotis as raj and always finishes her share.after 20 days if the number of rotis that were consumed during lunch by them together is 110 (excluding the wasted rotis)then find the number of rotis per meal that raj and riya take. how many rotis were wasted in 20 days

Answer 1

Let the number of rotis taken by Raj          = x
Let the number of rotis eaten by Raj          = x - 1/2
Let the number of rotis eaten by Riya        = x/2

Given: Total number of rotis eaten in 20 days = 110

i.e.,  20 (x - 1/2) + 20 (x/2) = 110
       20x -10 + 10x             =110                   (20x - 20/2  + 20x/2)
                 30x - 10           = 110
                               30x   = 110 + 10
                               30x   = 120
                                  x    = 120/30
                                  x    = 4

Therefore, the number of rotis
                                            taken by Raj     = 4
                                            eaten by Raj     = 4 - 1/2  = 3 1/2 (3.5)
                                           eaten by Riya    = 4/2 = 2

No. of rotis wasted in 20 days = 20 (1/2) =10

Answer 2

Let  Raj takes x number of rotis.
 Raj consumes x-0.5 rotis
Riya takes half of x = x/2 rotis
In 20 days they consume (x-0.5 + x/2)*20=110
                                  ⇒ 3x-1=11
                                  ⇒ x=4
Raj takes 4 rotis and Riya takes 2 rotis
No of rotis wasted is 0.5*20=10 rotis