A, B and C start a business with capital of Rs.8,00,000 , Rs.12,00,000 and Rs.15,00,000 respectively. A is working partner and takes 12\(\frac{1}{2}\)% of total profit as salary. If A received Rs. 5200 from the business as a profit then find the amount of total profit.

Rs. 16000

                  A         :       B           :         C

Inv.    :   800000   :   1200000   :    1500000

                  8         :       12         :        15

Profit:        8         :        12         :        15    =   35R    ......(i)

*If time is same then investment ratio becomes profit ratio*

Now, ATQ

⇒ 12\(\frac{1}{2}\) % profit taken by A and remaining 87\(\frac{1}{2}\)% (i.e. = 35R) is divided according to their profit ratio.

So,

12\(\frac{1}{2}\)% = \(\frac{1}{8}\) = \(\frac{5}{40}\)

⇒ Remaining = \(\frac{7}{8}\) = \(\frac{35}{40}\) ....(ii)

Compare (i) with (ii):

               A   :   B   :   C   ⇒    87\(\frac{1}{2}\)%   :  12\(\frac{1}{2}\) %(A)  :  Total

Profit:      8  :  12  :   15  ⇒     35          :      5          :      40

Hence,

A's total profit = 8R + 5R = 13R = 5200

⇒ 1R = 400

⇒ Total Profit = 40R = 40 × 400 = Rs.16000