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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% .
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 %
