Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% If A and B
are mixed in the ratio 3:2, and 5% if this ratio is 2:3. The cost prices, per kg, of A and B are in the
ratio
Answers
Answer:
The cost prices, per kg, of A and B are in the ratio 19:24
Step-by-step explanation:
Let say Cost Price of Tea A = A rs /kg
Cost Price of Tea B = B Rs/kg
A and B mixed in the ratio 3:2
Let say A = 3T then B = 2T
Total Cost Price = 3TA + 2TB Rs
Selling Price = 40 (3T + 2T) = 200T Rs
Profit = 10 % = (10/100) * (3TA + 2TB ) = (3TA + 2TB )/10
3TA + 2TB + (3TA + 2TB )/10 = 200T
=> 11(3TA + 2TB ) = 2000T
=> 33A + 22B = 2000
=> 66A + 44B = 4000
A and B mixed in the ratio 2:3
Let say A = 2T then B = 3T
Total Cost Price = 2TA + 3TB Rs
Selling Price = 40 (2T + 3T) = 200T Rs
Profit = 5 % = (5/100) * (2TA + 3TB ) = (2TA + 3TB )/20
2TA + 3TB + (3TA + 3TB )/20 = 200T
=> 21(2TA + 3TB ) = 4000T
=> 42A + 63B = 4000
66A + 44B = 42A + 63B
=> 24A = 19B
=> A/B = 19/24
=> A:B = 19 : 24
The cost prices, per kg, of A and B are in the ratio 19:24