AP_Quant_ShakulPathak.docx

General Instrucons: 1. While wring wring soluons soluons please please try try to provide provide step step by step step soluons soluons being being as elaborate elaborat e as possible possib le so that anyone can underst understand and the soluon. 2. While crean creang g quesons, quesons, please mae mae sure that that you create create quesons quesons !rom scratc scratch h and write soluons as per above guidelines. "lease #nd a$ached a #le containing #ve quesons o! %uantave &bility. &bility. 'tudy it well and write the detailed soluon o! each queson. (. 'ubse 'ubsequen quently tly,, you have to create create ) original original quesons quesons at the same level level o! di*culty. di*culty. "rovide opons, answers and soluons !or each queson. +. We are are also a$aching a$aching a sample soluon soluon !or !or your re!e re!erenc rence e so that you unders understand tand the ind o! eplanaon epected epected !rom you.

1. A shopkeeper shopkeeper buys buys 25 bags bags for Rs. Rs. 4000. Out Out of these, these, 5 bags are are bigger than than the the rest. At what price price should he sell the bigger big ger bags so as to earn a prot of 20! if he th sells the rest at "#4  of this price$ %&' Rs. 240 %&&' Rs. 140 %&&&' Rs. 2(0 %&)' Rs. 150 Ans* %&'

+oluon* -et us assue the selling price of each of the bigger bags / Rs.  According to the probles stateent * +elling rice of a saller bag will be Rs. "#4 %"#4 th of  ' 3ow,, it is gien that the rot ust be 20! . 3ow herefore,the total +elling rice should be such that the rot is 20! of the 6ost rice /7 herefore,the he rot is / 40008%20#100' / Rs. 900 herefore, herefor e, +elling rice/ 6ost rice : rot /7 Rs. 4000 : Rs. 900 / Rs. 4900 3ow,, it is gien that there are 25 bags of which 5 are bigger ones 3ow /7 20 of the bags are the saller ones . ;ence, the nal e

=or ruck  *   / #H%> : 40#@ '8ie%in ;rs'I / 1B50#H%> : 40#10'825I /(.9 =or ruck 6 *  6 / 6#H%> : 40#@6 '8ie%in ;rs'I/ 20>4#H%> : 40#B'824I K 9.2"4

=or ruck C *  C / C#H%> : 40#@C '8ie%in ;rs'I / 1912#H%> : 40#11'822I K 9.54(

6learly, A has the highest alue of the four . his gies us the answer as Opon %&' * ruck A . ". &f a tea tea of 4 persons persons is to to be selected selected fro fro 9 ales ales and 9 feales feales,, then in how how any ways can the selecons be ade to include at least 1 feale. %&' "500 %&&' 19(5 %&&&' 1(50 %&)' 3one of these Answer* %&&&' +oluon* De hae, otal nuber of @ales / 9 otal nuber of =eales / 9 De need to select a tea of 4 persons with at least one feale . o nd this easily, we can use a siple trick * he re eople%@ale:=eale' L otal 3uber of Days of +elecng 4 persons such that all are @ale. 3ow, otal 3uber of Days of +elecng 4 persons out of 1> people / 1>

64 / 1920

otal 3uber of Days of +elecng a tea of 4 @ales out of gien 9 @ales / 964 / (0 herefore, the otal 3uber of Days of +elecng a ea of 4 persons out of 9 @ales and 9 =eales under the gien condion that there is at least one =eale in the tea / 1>64 G 964 / 1920 L (0 / 1(50 . his gies us the the answer as Opon Opon %&&&' L 1(50 . 4. Aisha and and alak alak can do a piece of work work in 25 and 20 days days respecel respecely y. hey began began the work together but alak leM aMer soe days and Aisha copleted the rest of the work in 1> days. AMer how any days did alak leae$

%&' %&&' %&&&' %&)' Ans* %&&'

( days 4 days B days 12 days

+oluon* Aisha can do a piece of work in 25 Cays. herefore, herefor e, in one day she can do 1#25 of the work. alak can do the sae piece of work in 20 Cays. herefore, herefor e, in one day she can do 1#20 of the work. -et, us assue the nuber of days that passed before alak leM / ? Cays hen, we hae *G ?%%1#25':%1#20'' : 1>#25 / 1 %Dhole Dork' H +ince, =or ? Cays both Aisha and alak we working and for the rest 1> Cays only Aisha was working.I On soling we get *G ?%B#100' / B#25 Or, ? / 4 . his gies us the re %&&&' " %&)' 5 Answer * %&&&' +oluon * he rie =actoriWaon =actoriWaon of (5 / " 1 ? 52 he nuber of ways of decoposing (5 into two diPerent factors factors is the sae as nuber of factorss of (5 diided by 2 . factor %Q?planaon * Qach factor%of factor%of (5' diides (5 to gie another factor of (5 therefore, we ay think that the nuber of prie factors factors of (5 shall gie us the answer but it is iportant to note that in this process each set of two factors of (5 shall get repeated twice . ;ence, it is diided by 2' herefore 3uber of =actors Of (5 / %Q?ponent of " : 1'8%Q?ponent of 5 :1 ' H+ince, in the rie =actoriWaon =actoriWaon of the factors the power of " can be 0 or 1 %2 choices' and that of 5 can be 0,1 or 2 %" choices' I /2?" /> herefore , 3uber of Days it can be decoposed into two factors / >#2 / ". his gies us the answer as Opon %&&&' .

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