Correct Answer - Option 3 : 49 : 45
Given:
A and B are sold at Rs.60 per liter.
15% profit if sold in ratio A : B = 3 : 1
20% profit if sold at ratio A : B = 1 : 3
Calculation:
When A and B are mixed in the ratio 3 : 1,
then profit is 15%
⇒ CP = (3A + B)/(3 + 1)
⇒ 60/1.15 = (3A + B)/4
⇒ 240/1.15 = (3A + B)
⇒ 3A + B = 4800/23 ----(I)
When A and B are mixed in the ratio 1 : 3
then profit is 20%
⇒ CP = (A + 3B)/(3 + 1)
⇒ 60/1.2 = (A + 3B)/4
⇒ 240/1.2 = (A + 3B)
⇒ A + 3B = 200 ----(II)
Adding equation I and II,
⇒ 3A + B + A + 3B = 4800/23 + 200
⇒ 4A + 4B = 9400/23
⇒ 4(A + B) = 9400/23
⇒ A + B = 2350/23 ----(III)
Subtracting equation I and II,
⇒ 3A + B – A – 3B = 4800/23 – 200
⇒ 2(A – B) = 200/23
⇒ A – B = 100/23 ----(IV)
Adding equation III and IV
⇒ A + B + A – B = 2350/23 + 100/23
⇒ 2A = 2450/23
⇒ A = 1225/23
Subtracting equation III and IV
⇒ A + B – A + B = 2350/23 – 100/23
⇒ 2B = 2250/23
⇒ B = 1125/23
Now the ratio of A and B,
⇒ A : B = 1225/23 : 1125/23
⇒ A : B = 1225 : 1125
⇒ A : B = 49 : 45
∴ The ratio of CP of A and B is 49 : 45.