(**Part VII**) of **general aptitude for competitive exam** (IBPS and others) consists of shortcut methods, tips and tricks to solve question from Percentage, Simplification and Ratio and Proportion. Now (**Part VIII**) includes another three very important section from quantitative aptitudes including *“Boats and Streams”, “True Discount” and “Chain Rule”*.

Shortcut methods and tricks to solve questions from **‘****Boats and Streams’** are given below:

There are two type of streams: *Downstream and Upstream*

When you move along the direction of the stream, it’s called *Downstream*. In case you move in the opposite direction of the stream, it’s called *Upstream*.

If a boat moves with a speed of P km/h in still water with the speed of the stream Q km/h, then:

*Downstream* speed is: (P + Q) km/h

*Upstream* speed is: (P – Q) km/h

If the downstream speed is X km/h and upstream is Y km/h, then:

Speed in still water = (1 / 2) (X + Y) km/h

Rate of stream = (1 / 2) (X – Y) km/h

__Some other rules:____ __

**Rule 1: **

A person can row certain distance downstream in h_{1} hours and returns the same distance upstream in h_{2} hours. If the speed of stream is S km/h, then the speed of man in still water is given by:

S [(h_{2} + h_{1}) / (h_{2} – h_{1})] km/h

**Rule 2:**

A person can row in still water at s km/h. In a stream flowing at f km/h, if it takes the person t hours to row to a certain place and come back, then the distance between the two places is given by:

[{t (s^{2} – f^{2})} / 2s]

**Rule 3:**

A person can row in still water at s km/h. In a stream flowing at f km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance is given by:

[{t (s^{2} – f^{2})} / 2f]

**Rule 4:**

A person can row in still water at s km/h. In a stream flowing at f km/h, if he/she rows the same distance up and down the stream, then his average speed is given by:

**[(Upstream x Downstream) / Person’s speed in still water]**

= {(s – f) x (s + f)} / s km/h

= {(s^{2} – f^{2})} / s km/h

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Shortcut methods and tricks to solve questions from **‘****True Discount’** are given below:

__Let’s consider the following abbreviations:__

P.W = Present Worth of the products or materials

T= time

R% = Rate per annum

S.I = Simple Interest

T.D = True Discount, Interest on P.W (Present Worth)

Then the Amount = (P.W + T.D)

P.W = [(100 x Amount) / {100 + (R x T)}] = [Amount x T.D / (R x T)]

T.D = (P.W x R x T) / 100 = [(Amount x R x T) / {100 + (R x T)}]

Sum = (S.I x T.D) / (S.I – T.D)

(S.I – T.D) = S.I on T.D

In case of the Sum is put on the Compound Interest (C.I), then

P.W = [Amount / {1 + (R / 100)}^{T}]

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Shortcut methods and tricks to solve questions from **‘****Chain Rule’** are given below:

__Direct Proportion____ __

Two certain amount of things or quantities are said to be directly proportional to each other, when the increase or decrease of one quantity is related to the other quantity’s increase or decrease to the same extent.

E.g. Work is directly proportional to the number of men working at. More man power, more work amount.

__Indirect Proportion__

Two certain amount of things or quantities are said to be indirectly proportional to each other, , when the increase of one quantity is related to the other quantity’s decrease to the same extent.

E.g. Time taken to finish a certain amount of work by a person(s) is inversely proportional to the number of person(s) set to work on it. More man power, lesser time to be taken to finish it.

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