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Ratio, proportions

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  • sindhuja
    Hi all Kindly help me solve the following problem in the easiest way possible. A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of
    Message 1 of 13 , Jul 17, 2011
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      Hi all

      Kindly help me solve the following problem in the easiest way possible.

      A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

      choices:
      a.3150
      b.3350
      c.3250
      d.3050

      Thanks and Regards
      Sindhuja
    • boobalan bala
      hey...here is the answer let, a1=salary of anup last year b1=salary of bunty last year a2=salary of anup this year b2=salary of bunty this year a1/b1=2/3,
      Message 2 of 13 , Jul 22, 2011
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        hey...here is the answer
        let,
        a1=salary of anup last year
        b1=salary of bunty last year
        a2=salary of anup this year
        b2=salary of bunty this year

        a1/b1=2/3,  therefore  a1=(2/3)*b1.......................(1);
        a1/a2=3/4,  therefore  a1=(3/4)*a2........................(2);
        b1/b2=5/7,  therefore  b1=(5/7)*b2......................(3);
        b2-a2=1150;b2=a2+1150.....................................(4);

        substitute (2) & (3) in (1) and get a2
        substitute a2 in (4) you will get b2 =3150=ans ...option(a)...


        it will look long steps...if u practice it will be very easy
         
        Boobalan S,
        M.Tech,Process Design Engineer,
        +91-7598099662



        From: sindhuja <sindhujaa_2004@...>
        To: ascent4cat@yahoogroups.com
        Sent: Sun, 17 July, 2011 9:22:05 PM
        Subject: [2IIM CAT Prep] Ratio, proportions

         

        Hi all

        Kindly help me solve the following problem in the easiest way possible.

        A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

        choices:
        a.3150
        b.3350
        c.3250
        d.3050

        Thanks and Regards
        Sindhuja

      • ranjit eswaran
        Fastest way is to check which number is divisible by 7, since Bunty s salary has 5:7. Only number divisible by 7 is 3150. Quick way to check test of
        Message 3 of 13 , Jul 22, 2011
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          Fastest way is to check which number is divisible by 7, since Bunty's salary has 5:7. Only number divisible by 7 is 3150. Quick way to check test of divisibility by 7 for 4 digit numbers is multiply first 2 digits by 2 and add to last 2 digits. 31*2 + 50 = 112, further for 3 digits, 1*2+12=14, 1*3+4=7. I have an algorithm for n digits test of divisibility by 7. Anyway, since this is only divisible by 7 this has to be the answer. Further verifying, 5:7 is 2250:3150(450*5 and 450*7). So 3150-1150=2000. 3:4 is 1500:2000. And original ratio is 1500:2250 = 2:3. Hope this helps.
        • ranjit
          Fastest way is to check which number is divisible by 7, since Bunty s salary has 5:7. Only number divisible by 7 is 3150. Quick way to check test of
          Message 4 of 13 , Jul 22, 2011
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            Fastest way is to check which number is divisible by 7, since Bunty's salary has 5:7. Only number divisible by 7 is 3150. Quick way to check test of divisibility by 7 for 4 digit numbers is multiply first 2 digits by 2 and add to last 2 digits. 31*2 + 50 = 112, further for 3 digits, 1*2+12=14, 1*3+4=7. I have an algorithm for n digits test of divisibility by 7. Anyway, since this is only divisible by 7 this has to be the answer. Further verifying, 5:7 is 2250:3150(450*5 and 450*7). So 3150-1150=2000. 3:4 is 1500:2000. And original ratio is 1500:2250 = 2:3. Hope this helps.

            --- In ascent4cat@yahoogroups.com, "sindhuja" <sindhujaa_2004@...> wrote:
            >
            > Hi all
            >
            > Kindly help me solve the following problem in the easiest way possible.
            >
            > A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?
            >
            > choices:
            > a.3150
            > b.3350
            > c.3250
            > d.3050
            >
            > Thanks and Regards
            > Sindhuja
            >
          • Swati
            ... The answer will be a) 3150 In this the ans has to be a multple of 3,5 and 7 i.e. 105. Only one option satisfies this
            Message 5 of 13 , Jul 22, 2011
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              --- In ascent4cat@yahoogroups.com, "sindhuja" <sindhujaa_2004@...> wrote:
              >
              > Hi all
              >
              > Kindly help me solve the following problem in the easiest way possible.
              >
              > A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?
              >
              > choices:
              > a.3150
              > b.3350
              > c.3250
              > d.3050
              >
              >

              The answer will be a) 3150
              In this the ans has to be a multple of 3,5 and 7 i.e. 105. Only one option satisfies this
            • Naveenan Ramachandran
              Hi, A = 2x last year B = 3x last year A = 2x * 4 / 3 this year = 8x / 3 B = 3x * 7 / 5 this year = 21x / 5 Diff = (63x - 40x) / 15 = 1150 x = 1150 * 15 / 23 =
              Message 6 of 13 , Jul 22, 2011
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                Hi,

                A = 2x last year
                B = 3x last year

                A = 2x * 4 / 3 this year = 8x / 3
                B = 3x * 7 / 5 this year = 21x / 5

                Diff = (63x - 40x) / 15 = 1150

                x = 1150 * 15 / 23 = 50 * 15 = 750

                B's sal this year = 21 * 750 / 5 = 21 * 150 = Rs 3150

                What is the official answer ...
                --
                Regards,
                Naveenan
                2IIM Mumbai

                CAT 2012 Batch Starts July 31st

                CAT 2011 Crash - Starting Aug 7 - Batch of 8 students.

                Office: +91-80970-48484


                On Sun, Jul 17, 2011 at 9:22 PM, sindhuja <sindhujaa_2004@...> wrote:
                 

                Hi all

                Kindly help me solve the following problem in the easiest way possible.

                A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

                choices:
                a.3150
                b.3350
                c.3250
                d.3050

                Thanks and Regards
                Sindhuja





              • sindhuja ananthan
                Hi all PFB the solution given by a person Regards sindhuja ________________________________ From: Rahil Sahu To:
                Message 7 of 13 , Jul 22, 2011
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                  Hi all 

                  PFB the solution given by a person

                  Regards
                  sindhuja


                  From: Rahil Sahu <rahilsahu@...>
                  To: sindhujaa_2004@...
                  Sent: Fri, 22 July, 2011 10:56:03 AM
                  Subject: Re: [2IIM CAT Prep] Ratio, proportions

                  Assume
                  Anup - 2a, Bunty - 3a in 1st yr

                  2nd yr
                  Anup - 4x2a/3; Bunty - 7x3a/5

                  21a/5 - 8a/3 = 1150
                  Solve for a, you get a =750

                  Bunty in 2nd yr = 21a/5 = 3150
                   

                  Rahil Sahu
                  Naval Architect
                  VEDAM Design & Techinal Consultancy Pvt. Ltd.

                  Ph - 91-22-6710 9192

                  www.vedamindia.com




                  From: sindhuja <sindhujaa_2004@...>
                  To: ascent4cat@yahoogroups.com
                  Sent: Sun, 17 July, 2011 9:22:05 PM
                  Subject: [2IIM CAT Prep] Ratio, proportions

                   

                  Hi all

                  Kindly help me solve the following problem in the easiest way possible.

                  A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

                  choices:
                  a.3150
                  b.3350
                  c.3250
                  d.3050

                  Thanks and Regards
                  Sindhuja

                • sindhuja ananthan
                  Hi thanks for the solution. @ all: PFB another solution for the same question Regards sindhuja ________________________________ From: boobalan bala
                  Message 8 of 13 , Jul 22, 2011
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                    Hi

                    thanks for the solution.

                    @ all: PFB another solution for the same question

                    Regards
                    sindhuja


                    From: boobalan bala <boobalanprpc@...>
                    To: sindhujaa_2004@...
                    Sent: Fri, 22 July, 2011 2:12:12 PM
                    Subject: Fw: [2IIM CAT Prep] Ratio, proportions


                     
                    Boobalan S,
                    M.Tech,Process Design Engineer,
                    +91-8688196956


                    ----- Forwarded Message ----
                    From: boobalan bala <boobalanprpc@...>
                    To: ascent4cat@yahoogroups.com
                    Sent: Fri, 22 July, 2011 2:09:16 PM
                    Subject: Re: [2IIM CAT Prep] Ratio, proportions

                    hey...here is the answer
                    let,
                    a1=salary of anup last year
                    b1=salary of bunty last year
                    a2=salary of anup this year
                    b2=salary of bunty this year

                    a1/b1=2/3,  therefore  a1=(2/3)*b1.......................(1);
                    a1/a2=3/4,  therefore  a1=(3/4)*a2........................(2);
                    b1/b2=5/7,  therefore  b1=(5/7)*b2......................(3);
                    b2-a2=1150;b2=a2+1150.....................................(4);

                    substitute (2) & (3) in (1) and get a2
                    substitute a2 in (4) you will get b2 =3150=ans ...option(a)...


                    it will look long steps...if u practice it will be very easy
                     
                    Boobalan S,
                    M.Tech,Process Design Engineer,
                    +91-7598099662



                    From: sindhuja <sindhujaa_2004@...>
                    To: ascent4cat@yahoogroups.com
                    Sent: Sun, 17 July, 2011 9:22:05 PM
                    Subject: [2IIM CAT Prep] Ratio, proportions

                     

                    Hi all

                    Kindly help me solve the following problem in the easiest way possible.

                    A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

                    choices:
                    a.3150
                    b.3350
                    c.3250
                    d.3050

                    Thanks and Regards
                    Sindhuja

                  • Monisha Raj
                    lets anup s last yr salary be 2x and bunty s last yr salary be 3x......let this yr salary of anup and bunty be a and b respectively........now (2x)/a=3/4
                    Message 9 of 13 , Aug 3, 2011
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                      lets anup's last yr salary be 2x and bunty's last yr salary be 3x......
                      let this yr salary of anup and bunty be a and b respectively........
                      now (2x)/a=3/4 ->(1)
                              (3x/b)=5/7 ->(2)
                      then a=8x/3
                             b=21x/5
                        difference in dis yr salary ie a-b=1150
                      (8x/3) - (21x/5)=1150

                      solving we get x=750
                         then bunty's dis yr salary  is 21x/5  = 3150
                    • mohit gupta
                      data sufficiency If N is a natural number then number of factors of N^2 is ... A. N has 12 factors. B. N^3 has 70 factors. pls ans with xplanation
                      Message 10 of 13 , Aug 16, 2011
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                        data sufficiency
                        If N is a natural number then number of factors of N^2 is ...

                        A. N has 12 factors.
                        B. N^3 has 70 factors.



                        pls ans with xplanation
                      • Rajesh Balasubramanian
                        N has 12 factors = N can be of the form p^11 or p*q^5 or p^2 * q^3. So, this is not sufficient N^3 has 70 factors 70 can be written as 70 * 1 = N^3 = p^69
                        Message 11 of 13 , Aug 16, 2011
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                          N has 12 factors => N can be of the form p^11 or p*q^5 or p^2 * q^3. So, this is not sufficient
                          N^3 has 70 factors
                           
                          70 can be written as
                          70 * 1 => N^3 = p^69 possible => N = p^ 23
                          35 * 2 => N^3 =  p^34 * q  Not possible as this cannot be a perfect cube
                          5 * 14 => N^3 =  p^4 * q^13 Not possible as this cannot be a perfect cube
                          7 * 10 => N^3 = p^6 * q ^ 9 Possible => N = P^2 * q^3
                           
                          So, this alone is not sufficient.
                           
                          Both combined together, we can say N has to be of the form p^2 * q^3 and therefore number of factors of N^2 can be found.
                           
                          Good question, but to be honest I do not think CAT will ask a question even as tough as this.
                           
                          Cheers,
                          Rajesh
                          2IIM


                           
                          On Wed, Aug 17, 2011 at 4:38 AM, mohit gupta <mohit_luvkush@...> wrote:
                           

                          data sufficiency
                          If N is a natural number then number of factors of N^2 is ...

                          A. N has 12 factors.
                          B. N^3 has 70 factors.



                          pls ans with xplanation


                        • mohit gupta
                          dere r 6 letters and 6 addressed envelops... what is the proabability that exactly 3 are in wrong envelops..
                          Message 12 of 13 , Aug 18, 2011
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                            dere r 6 letters and 6 addressed envelops...


                            what is the proabability that exactly 3 are in wrong envelops..


                          • Yuv Bansal
                            I think it should be 2400.. because you take 3 letters at random which is 6C3 then you multiply by the number of ways each will go in so 6*5*4 6C3*6*5*4 = 2400
                            Message 13 of 13 , Aug 19, 2011
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                              I think it should be 2400..
                              because you take 3 letters at random which is 6C3 then you multiply by the number of ways each will go in so 6*5*4
                              6C3*6*5*4 = 2400


                              From: mohit gupta <mohit_luvkush@...>
                              To: "ascent4cat@yahoogroups.com" <ascent4cat@yahoogroups.com>
                              Sent: Friday, August 19, 2011 1:11 AM
                              Subject: Re: [2IIM CAT Prep] Ratio, proportions

                               
                              dere r 6 letters and 6 addressed envelops...


                              what is the proabability that exactly 3 are in wrong envelops..




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