A recap of the Basic Concepts to get going!


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.


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
∴ 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?


For such type of questions, remember the formula;
Quantity left = [x(1-y/x)²] units
Where; x is the total liquid initially
y is the amount taken out
n is the number of operations
∴ Petrol left = [60(1-10/60)²]
= 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?


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

= (2/5×5+1/5×15)/(3/5×5+4/5×15)
= (2+3)/(3+12)
= 5/( 15)
= 1:3


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

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

We can represent it as below:

Concept 2(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?


By the rule of alligation,

1∴ 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.


By the rule of alligation,

2Ratio = 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?


His average speed for entire journey = 984/12
= 82 kmph

By the rule of alligation:

3Ratio = 68:32
He must have travelled (32/(68+32)) × 12 = 3.84 hours at the speed of 150 kmph
So distance travelled = 576 km

All the Best!
Happy Practice!! 🙂


Time Speed & Distance

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