Shortcuts in solving aptitude-7

Allegation or Mixtures

Important Facts and Formulae:

1. Allegation: It is the rule that enables us to find the Ratio in which two of more ingredients at the given price must be mixed to produce a mixture of a desired price.

2. Mean Price: The cost price of a unit quantity of the mixture is called the mean price.

3. Rule of Allegation: If two ingredients are mixed then

Quantity of Cheaper / Quantity of Dearer = (C.P of Dearer – Mean Price) /(Mean Price–C.P of Cheaper).

C.P of a unit quantity of cheaper(c)    C.P of unit quantity of dearer (d)

                                                  Mean Price (m)

                                 (d-m)                                               (m-c)

        Cheaper quantity: Dearer quantity = (d-m):(m-c)

4. Suppose a container contains x units of liquid from which units are taken out and replaced by water. After n Operatations the quantity of pure liquid = x (1 – y/x)n units.

To exercise some problems on allegation or mixtures visit here

Boats and Streams

Important facts:  

1)In water, the direction along the stream is called downstream.

2)Direction against the stream is called upstream.

3)The speed of boat in still water is U km/hr and the speed of

stream is V km/hr then

speed downstream =U + V km/hr

speed up stream = U – V km/hr

Formulae:

If the speed downstream is A km/hr and the speed up stream is

B km/hr then speed in still water = ½(A+B) km/hr

rate of stream =1/2(A-B) km/hr

To exercise some problems on Boats and streams visit here