Question

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​

Answer 1

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​