*A recap of the Basic Concepts to get going!*

*A recap of the Basic Concepts to get going!*

*Concept-1:*

*Concept-1:*

**1. The ratio of milk & water in mixture is 5:1 respectively. If the total mixture is 48 litres, then find the new ratio of milk to water when 12 litres of water be added to the mixture.**

**Solution-1:**

Quantity of milk in the mixture = 5* 48/6 = 40 litres

Quantity of water in the mixture = 8 litres

After addition of 12 liters of water;

Total water in the mixture = 20 litres

ā“ New ratio of milk to water = 40 : 20

= 2 : 1

**2. A tank contains 60 L of Petrol. From this tank 10 L of Petrol was taken out and replaced by Diesel. This process was repeated one more time. How much Petrol is left in the tank now?**

**Solution-2:**

For such type of questions, remember the formula;

**Quantity left = [x(1-y/x)Ā²] units**

Where; x is the total liquid initially

y is the amount taken out

n is the number of operations

ā“ Petrol left =** [60(1-10/60)Ā²]**

= 60* 5/6*5/6

= 41.66 litres

**3. In two solutions the ratio of Green and Blue colour is 2:3 & 1:4 respectively. If 5 kg of the first solution & 15 kg of the second solution are mixed together, then find the ratio of Green colour to Blue colour in the new solution?**

**Solution-3:**

(Green colour in new solution)/(Blue colour in new solution) = (Green in 1st + Green in 2nd)/(Blue in 1st + Blue in 2nd)

= (2/5Ć5+1/5Ć15)/(3/5Ć5+4/5Ć15)

= (2+3)/(3+12)

= 5/( 15)

= 1:3

**Concept-2: **

**Concept-2:**

Rule of allegation: If 2 ingredients are mixed in a ratio then,

**(Quantity of cheaper)/(Quantity of dearer) = (C.P.of dearer ā Mean price)/(Mean price ā C.P.of cheaper)**

We can represent it as below:

**(Cheaper Quantity)/(Dearer Quantity ) = (d-m)/(m-c)**

Remember this basic rule of alligation, It will be useful in almost all the problems of alligations.

** 1. In what ratio must Sugar at Rs.6.50 per kg be mixed with Sugar at Rs.9 per kg so that the mixture be worth Rs.7 per kg?**

**Solution-1:**

By the rule of alligation,

ā“ Reuired ratio = 200 : 50

= 4:1

**2. A vendor has 42 kg of Tea, a part which he sells at a profit of 20% & rest at a profit of 26%, he gains 24% on the whole. Find the quantity of Tea sold at 26% profit.**

**Solution-2:**

By the rule of alligation,

Ratio = 2:4

= 1:2

Therefore, the quantity sold at 26% profit

= 2/3*42

= 28 Kg

**3. A Truck driver covers 984 km partly at a speed of 50 kmph and partly at a speed of 150 kmph, in 12 hours over all. What is the distance covered at the speeds of 150 kmph?**

**Solution-3:**

His average speed for entire journey = 984/12

= 82 kmph

By the rule of alligation:

Ratio = 68:32

He must have travelled (32/(68+32)) Ć 12 = 3.84 hours at the speed of 150 kmph

So distance travelled = 576 km

**All the Best! **

**Happy Practice!! š**