Question
A man buys 3 type-I cakes and 6 type-II cakes for Rs.
900. He sells type-I cakes at a profit of 15% and type-II cakes at a loss of 10%. If his overall profit is Rs. 30, the cost price (in Rs.) of a type-I and a type-II cake is:Solution
ATQ, Total profit = 30 Average profit = 30/900 × 100 = 10/3% Using allegation Method 15   -   10    10/3 40/3    35/3 Ratio of type-1 cakes to type-2 cakes = 40/3 : 35/3 = 8 : 7 ⇒ 8 + 7 = 15 unit ⇒ 15 unit = 900 ⇒ 1 unit = 60 ⇒ 8 unit = 480 ⇒ 7 unit = 420 Total cost of type-1, 3 cakes = 480 Cost of type-1, 1 cake = 480/3 = 160 Total cost of type-2, 6 cakes = 420 Cost of type-2, 1 cake = 420/6 = 70
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