(Part VIII) of general aptitude for competitive exam (IBPS) consists of shortcut methods, tips and tricks to solve question from Boats and Streams, True Discount and Chain Rule. Now (Part IX) includes another three very important section from quantitative aptitudes including “Partnership”, “Surds and Indices” and “Pipes and Cistern”.
Shortcut methods and tricks to solve questions from ‘Partnership’ are given below:
When two or more than two persons run a business jointly they are called ‘partners’, and the deal is known as ‘partnership’.
Ration of Divisions of Gains
When all partners invests for the same time period, then the gain or loss is distributed between them in the ratio of their investments.
Suppose, P and Q invests Rs. a and b respectively for a year in a business, then at the end of the year:
(P’s share of profit) : (Q’s share of profit) = x:y
When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Gain or loss is divided in the ratio of these capitals.
Suppose P invests Rs. m for y months and Q invests Rs. n for z months then,
(P’s share of profit) : (Q’s share of profit) = (xm : yn)
‘Working and Sleeping Partners’ concept has already been discussed in previous post.
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Shortcut methods and tricks to solve questions from ‘Surds and Indices’ are given below:
Some important formulas for ‘Surds and Indices’ are given below:

a^{m} x a^{n} = a^{(m +n)}

a^{m} / a^{n }= a^{(m n)}

a^{mn} = a^{mn}

(ab)^{n} = a^{n}b^{n}

(a/b)^{n} = a^{n }/ b^{n}

a^{0} = 1
Surds
Let x be the rational number and n be a positive integer such that x^{(1 / n) }= ^{n}√x
Then, n√x is called a surd of order n.
Laws of Surds
The formulas are shown in the below diagram:
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Shortcut methods and tricks to solve questions from ‘Pipes and Cistern’ are given below:
Few important things to remember while try solving the aptitude questions from this section. They are described below:
Inlet
When a pipe is filling the tank or cistern or reservoir it’s connected with, is known as inlet.
Outlet
When a pipe is emptying the tank or cistern or reservoir it’s connected with, is known as outlet.
If a pipe can fill a tank or cistern or reservoir in h hour, then:
part filled in 1 hr. = 1 / h.
If a pipe can empty a tank or cistern or reservoir in p hour, then:
part emptied in 1 hr. = 1 / p
If a pipe can fill the tank or cistern or reservoir in m hrs. and then another tank or cistern or reservoir in n hrs. (where n > m), then on opening both the pipes:
the net part filled in 1 hr. = [(1 / m) – (1 / n)]
If a pipe can fill the tank or cistern or reservoir in m hrs. and then another tank or cistern or reservoir in n hrs. (where m > n), then on opening both the pipes:
[(1 / n) – (1 / m)]
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