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Quantitative Aptitude, Part - I

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Published in: Mathematics
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Arithmetical Ability ( KEY TOPICS )

Arun M / Faridabad

4 years of teaching experience

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Teaches: Mathematics, IIT JEE Mains

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  1. Quantitative Aptitude, Part - 1 ( Arithmetical Ability ) February 28 2016 KEY TOPICS
  2. TIME AND DISTANCE : Speed = ( Distance / Time ) Time = ( Distance / Speed ) Distance = ( Speed x Time ) 1 km / hr = (5 / 18) m/ sec AND 1 m/ sec = (18 / 5) km / hr Let ratio of Speed of X and Y is n : m, then ratio of the times taken by them to cover the same distance is m : n Average Speed = ( Total Distance / Total Time ) TIME AND WORK : If B can do a piece of work in m days, then B's I day's work 1 / m If B' s I day's work — 1 / m, then B can finish the work in m days. If X is thrice as good a workman as Y, then . Ratio of work done by X and Y = 3 : 1 Ratio of times taken by X and Y to finish a work = 1 : 3 If A's I day's work — 1 / m and B' s I day's work = 1 / n then . (A + B )'s I day's work — 1 / (m+n) Also Both A and B will finish the work in (m + n ) days PIPES AND CISTERN : INLET : Pipe used for filling a tank or cistern. OUTLET : Pipe used for emptying a tank or cistern. If a pipe can fill a tank in n hours, than : part filled in 1 hour = 1 / n If a pipe can empty a tank in m hours, than : part emptied in 1 hour = 1 / m If a pipe can fill a tank in n hrs. and another pipe can empty the full tank in m hours ( where m > n ), then on opening both the pipes, the net part filled in 1 hour = ( l/n — l/m ). If a pipe can fill a tank in n hrs. and another pipe can empty the full tank in m hours ( where m < n ), then on opening both the pipes, the net part emptied in 1 hour = ( l/m — l/n ). PROBLEMS ON TRAINS : Time taken by a train of length L m to pass a pole / standing man / a signal etc. is equal to the time taken by train to cover L meters. Time taken by a train of length L m to pass a stationary object of length I meters is equal to the time taken by train to cover ( L + I ) meters. If two trains ( or two bodies ) are moving in the same direction at u m/sec and v m/sec ( where u > v ), then their relative speed is = ( u — v ) m/sec.
  3. If two trains ( or two bodies ) are moving in the opposite directions at u m/sec and v m/sec, then their relative speed is = ( u + v ) m/sec. If two trains of length L m and M m are moving in the same direction at u m / sec. and v m/sec., then the time taken by the faster train to cross the slower train = (L + N)/ (u —v) sec. If two trains of length L m and M m are moving in the opposite direction at u m / sec. and v m/sec., then the time taken by the two trains to cross each other = (L + N)/ (u + v) sec. If two trains of length L m and M m are moving in the opposite direction at u m / sec. and v m/sec., then the time taken by the two trains to cross each other = (L + N)/ (u + v) sec. If two trains ( or bodies ) start at the same time from points A and B towards each other and after crossing they take x and y sec. in reaching B and A respectively , = (y 1/2 : x 1/2) then (A's speed) : (B's speed) BOATS AND STREAMS : DOWNSTREAM : Direction along the stream. UPSTREAM : Direction against the stream. If speed of a boat in STILL water is u m/sec and the speed of the stream is v m/sec, then . Speed Downstream = (u + v ) m/sec. Speed Upstream = ( u — v ) m/sec. Also Speed in STILL water = 1 / 2 x ( Speed downstream + Speed upstream ) Speed of Stream = 1 / 2 x ( Speed downstream - Speed upstream ) ALLIGATION OR MIXTURE : ALLIGATION : Is the Rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price. MEAN PRICE : The cost price of a unit quantity of the mixture is called the mean price. RULE OF ALLIGATION . ( Quantity of cheaper ingredient / Quantity of dearer ingredient ) = ( C.P of dearer ingredient - Mean price ) / (Mean price - C.P of cheaper ingredients ) If a container contains a units of a liquid from which b units are taken out and replaced by water. After n such operations, the quantity of pure liquid = [ x { 1 — (y/x) n } ] units.

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