Problem:

Two liquids are mixed in the ratio of 5:3, and the vendor gains 16.67% by selling the mixture at Rs. 12.25/litre. If the first liquid costs Rs. 4/litre more than the second, find the CP of each liquid.

Solution:

Step 1: Understanding the problem

- Two liquids are mixed in the ratio of 5:3.
- The vendor gains 16.67% by selling the mixture at Rs. 12.25/litre.
- The first liquid costs Rs. 4/litre more than the second.
- We need to find the CP of each liquid.

Step 2: Finding the CP of the mixture

- Let the CP of the mixture be Rs. x/litre.
- The vendor gains 16.67%, which means he sells at a profit of 1/6 of the CP.
- Selling price (SP) of 1 litre of the mixture = CP + Profit
- SP = x + (1/6)x = (7/6)x
- Given, SP = Rs. 12.25/litre
- (7/6)x = 12.25
- x = (6/7) * 12.25
- x = Rs. 10.5/litre

Therefore, the CP of the mixture is Rs. 10.5/litre.

Step 3: Finding the CP of each liquid

- Let the CP of the second liquid be Rs. y/litre.
- The CP of the first liquid is Rs. (y + 4)/litre (given).
- The liquids are mixed in the ratio of 5:3.
- Let the quantity of the first liquid be 5x and that of the second liquid be 3x.
- Total quantity = 5x + 3x = 8x
- CP of the mixture = (5x * (y + 4)) + (3x * y) / 8x
- 10.5 = (5y + 20 + 3y) / 8
- 84 = 8y + 20
- 8y = 64
- y = 8

Therefore, the CP of the first liquid is Rs. 12/litre and that of the second liquid is Rs. 8/litre.

Step 4: Verification

- The CP of the mixture is (5 * 12 + 3 * 8) / 8 = Rs. 10.5/litre.
- The vendor gains 16.67% by selling at Rs. 12.25/litre.
- Profit % = (SP - CP) / CP * 100
- Profit % = (12.25 - 10.5) / 10.5 * 100
- Profit % = 16.67%

Therefore, the solution is verified.

Conclusion:

- The CP of the first liquid is Rs. 12/litre and that of the second liquid is Rs. 8/litre.
- The CP of the mixture is Rs. 10.5/litre.