(i) Notes that the amounts Manan is paid for each painting forms an AP.
Takes a = 6000, d = 200 and n = 25 to find the amount as
6000 + (25 - 1)200 = Rs 10800.
(ii) Finds the total amount earned by Bhima as follows:
S50 = 50/2 [2(4000) + (50 - 1)(400)]
Solves the above expression to find the total amount as Rs 6,90,000.
(iii) Frames equation as follows:
6000 + (n - 1)200 = 4000 + (n - 1) 400
Solves the above equation to find the value of n as 11.
Writes that, since they both earn the same amount for the 11th painting, as Bhima's increment is more, Bhima gets more money than Manan for the 12th painting.
OR
Assumes that the number of paintings required is n. Frames equation as follows:
Sn(Manan) = Sn(Bhima)
=> n/2 [2(6000) + (n -1)200]
= n/2 [2(4000) + (n -1)400]
Solves the equation from step 1 to find n as 21.