r = profit of unit principal at unit time
A = principal with profit after time n.
Example 1. For a function of Annual Sports, members of an association made a
budget of Tk. 45000 and divided that every member would subscribe equally. But 5
members refused to subscribe. As a result, amount of subscription of each member
increased by Tk. 15 per head. How many members were in the association?
Solution : Let the number of members of the association be x and amount of
subscription per head be Tk. q Then total amount of subscription A = Tk. qx.
Actually numbers of members were (x 5 )and amount of subscription per head
became Tk. (q 15 ).
Then, total amount of subscription = Tk. (x 5 )(q 15 )
By the question, qx (x 5 )(q 15 )..........(i)
and qx 45 , 000 ..........(ii)
From equation (i), we get, qx (x 5 )(q 15 )
or, qx qx 5 q 15 x 75
or, 5 q 15 x 75 5 ( 3 x 15 )
? q 3 x 15 ...........(iii)
Putting the value of q in equation (ii),
( 3 x 15 )ux 45000or, 3 x^2 15 x 45000
or, x^2 5 x 15000 [dividing both sides by 3]
or, x^2 5 x 15000 0
or, x^2 125 x 120 x 15000 0
or, x(x 125 ) 120 (x 125 ) 0
or, (x 125 )(x 120 ) 0
?x 125 0 or, x 120 0
If x 125 0 ,x 125
Again, if (x 120 ) 0 , x 120
Since the number of members i.e,, x cannot be negative, xz 120.
?x 125
Hence, number of members of the association is 125.
Example 2. Rafiq can do a work in 10 days and shafiq can do that work in 15 days.
In how many days do they together finish the work?