The ratio of the selling price of 3 articles A,B, and C is 8:9:5 and the ratio of percentage profit is 8:7:14 respectively. if the profit percent of A is 14.28% and the cost price of B is Rs.400, what is the overall percentage gain? plz suggest any shortcut method for this.

Given that the Selling Price(SP) of articles A, B and C are in the ratio 8 : 9 : 5. Let SP be 8q, 9q and 5q. ----------------> eq.1 Given, Profit percentage = 8 : 7 : 14. Let their profit percentage be 8p%, 7p% and 14p%. A's profit percent = 14.28% 8p% = 14. 28% p = 14.28/8 = 1.78. Then, B's profit percent = 7p% = 7 × 1.78 = 12.50% Profit Percentage of C = 14p = 14 × 1.78 = 25% But given that Cost Price of B = Rs. 400. SP of B = 400 + 12.50%(400) = Rs. 450. So, 9q = 450; q = 50. Selling Price of A = 8q = 8 × 50 = Rs. 400. SP of C = 5q = 5 × 50 = Rs. 250. Total SP = 450 + 400 + 250 = Rs. 1100. Let CP of A = a a = 400 – 14.28% of a; a = 400 – (14. 28a /100) 100a = 40000 – 14.28a => 114.28a = 40000 a = Rs. 350. Let CP of C = c c + 25% of c = 250 125c = 25000 c = Rs. 200. Total CP = 400 + 350 + 200 = Rs. 950. Profit = SP - CP = 1100 - 950= 150. Overall % Profit = (150 *100) /950 = 15.78% .

Any shortcut?

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SP of A = (1 +1/7) * CP of A = (8/7) * 400 = 3200/7 Using the given ratios for SPs find the other SP -----> SP of B = 9/8 * SP of A = 3600/7 SP of C = 5/8 * SP of A = 2000/7 Similarly, find the profit percentages for B & C using the ratio given. We know the profit % for A is 1/7 Profit percentage for B = 7/8 * 1/7 = 1/8 Profit percentage for C = 14/8 * 1/7 = 1/4 Using this profit percentage calculate CP of B and CP of C , CP of B = ( 1/(1+1/8) ) * SP of B = 3200/7 CP of C = ( 1/(1+1/4) ) * SP of C = 1600/7 Overall percentage gain = ( Sum of SP of (A,B,C) - Sum of CP of (A,B,C) ) / ( Sum of Cp of (A,B,C) ) = ( 8800/7 - 7600 /7 ) / (7600/7) = 3/19 = 15.789 %

SP==8 9 5 P == 8 7 14 8 = 14.28% =1/7 7 = 12.5% = 1/8 14 = 25% = 1/4 SP -- 8 9 5 CP -- 7 8 4 8+9+5=22 7+8+4=19 (3/19)*100 = 15.78