**Qu.1) The ratio of quantities of sugar, in which sugar costing Rs. 20 per kg and Rs. 15 per kg should be mixed so that here will be neither loss nor gain on selling the mixed sugar at the rate of Rs. 16 per kg is**

Given: Cost of sugar1 = Rs. 20 per kg

Cost of sugar 2 = Rs.15 per kg

Cost of mixed sugar = Rs. 16 per kg

According to the question, when there is no profit no loss,

SP = CP

CP of mixed sugar = Rs. 16 per kg

**Ans. Ratio of quantities of sugar = 1: 4**

**Qu.2) The acid and water in two vessels A and B are in the ratio 4: 3 and 2: 3. In what ratio should the liquids in both the vessels should be mixed to obtain a new mixture in vessel C containing half acid and half water**

Given: acid: water –

Vessel A = 4: 3

Vessel B = 2: 3

In vessel C acid and water should be in equal ratio I.e. 1/ 2

Now using the allegations,

Ratio of quantity = 1/ 10: 1/ 14

= 14: 10

= 7: 5

**Ans. Ratio of acid and water is 7: 5**

**(03) A container contains 60 kg of milk. From this container 6 kg of milk was taken out and replaced by water. This process was further repeated by 2 times. The amount of milk left in the container is:**

Given: Total quantity of milk = 60 kg

Taken out milk = 3 times

To find : final quantity

Ans. The amount of milk left in the container is 43.74 kg.

**(04) A can contains a mixture of two liquids A and B in the ratio 7: 5. When 9 litres of mixture are drained off and the can is filled with B, the ratio of A and B becomes 7: 9. How many litres of liquid A was contained by the can initially?**

Initial Ratio = 7: 5; total =12

Final ratio = 7: 9; total = 16

Taken out = 9 litres

Here the **ratio value **of liquid A is same but **ratio value** of liquid B is increasing i.e.

Increment of 4 units = 9 litres

1 unit = 9/ 4 litre

12 units = (9/4) x 12 = 27 litres

Initially solution = 27 + 9 = 36 litres

Quantity of liquid A initially = (7/ 12) x 36

= 21 litres

**Ans. 21 litres of liquid A was contained by the can initially.**

**(05)** **A jar contained a mixture of two liquids of A and B in the ratio 4: 1. When 10 litres of the mixture was taken out and 10 litres of liquid B was poured into the jar. This ratio became 2: 3. The quantity of liquid A contained in the jar initially was:**

**When any quantity of mixture is taken out from the mixture then the ratio of the remaining mixture remains the same = 4: 1**

Given : Initial Ratio = 4: 1

Final Ratio = 2: 3

Now mixture is taken out and liquid B is added. So, make A proportion equal we can do following calculations:

Final Ratio x 2 = 4: 6

NOW, Initial Ratio =4 : 1

And, Final Ratio = 4: 6

So there has been increase of 5 units in liquid B, which is caused by addition of 10 liters

5 units = 10 litres (since increment of 5 units from initial to final value of B)

1 unit = 2 litres

Quantity of solution = 4 + 6 = 10 units

= 10 x 2 = 20 litres

Quantity of A initially = 4/ (4 + 1) x 20

= (4/5) x 20 litres

= 16 litres