**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*
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