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Class 8 R S Aggarwal Maths solutions

Contents

10.      Profit and Loss

            Discount, VAT

11.      Compound Interest EX – 11A, B, C

 

 

 

 

 

Q19.  Let the CP of chair be x.  Then ATQ,

            SP at 15% gain – SP at 8% gain = Rs. 56.

π      -    = 56.      =>   = 56     => x = 800.

                       

Q20.  ATQ,  10% of x + 65 = 14% of x  

π       + 65   =         =>  -  +    = - 65.   => -   = - 65

π       =  Rs. 1625.

 

 Q21.       Total CP = 40 X 6.25 + 30 X 7 = 250 + 210 = 460.

                        Total SP = 460 X     = 23 X 21.   

Rate =  =   =   = Rs. 6.9/kg.

 

Q22.  ATQ, SP of !st bat = 560 + 15% of 560     =   560 +  X 560     = 560 + 84 = 644.

              Now, SP of 2nd bat =  240 – 5% of 240     =  240 -  X  240      = 240 -12   = 228.

            Hence total CP = 560 + 240 = 800   & Total SP   = 644 + 228     = 872. Since, SP > CP.

            It is gain.  Gain = 872 – 800 = 72.   Hence,  gain% =  X100   =  9%.

 

                        

Q23.   ATQ,  [i] 1st shirt   Total CP = 725.       Gain  = 8%

π    SP =   X 725  = 27 X 29  =Rs. 783.    

π    Now, 2nd  shirt CP = 725, loss = 4%

π    SP =   X 725  =  24 X 29 = Rs. 696.

π     Now, Total CP = 725 X 2= 1450. Total SP = 783 + 696 = 1479.

Since, SP > CP. It is gain.  Gain = 1479 – 1450 = 29.

Hence, gain% =   X 100   = X 100  =       2%.

           

Q24.   ATQ, Total CP = 200 X 25  = 5000        gain =8% on total investment.

            SP =  X 5000   = 5400.

            Now, CP of 80 kg rice = 80 X 25 = 2000.

                       SP of 80kg rice at 10% gain =   X 2000 = 2200.

            Now,  CP of 40 kg rice  = 40 X 25 = 1000

                       SP of 40kg rice at 4% loss            =   X 1000   = 960.

               Now, remaining quantity of rice = 200 – (80 + 40) = 80kg.

                        CP of 80 kg rice = 80 X 25 = 2000. 

                        SP of 80kg rice = Total Sp SP of 120kg rice              

            = 5400 – 3160 = 2240.   Hence,  rate =    =28/kg.

 

 Q25.     Let CP be x , then ATQ,  CP – x & SP =     

   Gain = SP –CP =  - x =  =  

              Gain% =  X 100  =   X 100   =   =  33 %.

 

Q26.   Let the CP be x. Then ATQ,        CP = x   & SP =  

π     Gain = (SP -CP) =  - x =  

π    Hence, gain% =  X 100      = 20%.

 

Q27.    Let the CP of each gram be Re 1. Then, the CP of 960g = Rs.960

            And the SP of 960 g = Rs. 1000.

            Gain = SP – CP = 1000 – 960 =Rs.40. Hence, Gain% =  X 100 =  = 4  %.

 

 Q27.      ATQ,     SP of umbrella = 115.20     & loss = 10%     So, CP  =    X SP  

            CP  =    X 115.20 = Rs. 128.

            Now, SP at 5% gain  =   X CP    =   X 128 =  = 134.40

 

  Q28.     ATQ,  SP of bouquet  = Rs. 322, gain = 15%, then, CP =   X 322. = Rs. 280.

            Now, SP at 25% gain =   X 280  =  X 280  =  Rs.350.

                       

Q29.    ATQ,  SP of radio = 3120, loss = 4%.  Then, CP  =    X SP

            =    X 3120  = 25 X 130 = Rs. 3250.    Again, Since, SP > CP . It is gain.

            Gain = 3445 – 3250 = 195. Hence, gain% =  X 100 = 6%.

 

 Q30.     ATQ, SP of 1st  saree = 2185, loss = 5%,  Then,  CP  =    X 2185 = 2300

              SP of 2nd saree = 2185, gain = 15%,  Then, CP =   X 2185 =  1900.

            Hence, CP of both saree = 2300 + 1900 = 4200.

            And  SP of both saree = 2185 X2 = 4370.  Since, SP > Cp. It is gain.

            Gain = 4370 – 4200 = 170.  Hence, gain% =  X 100 =   = 4 .

          

 Q31.     ATQ, SP of 1st fans = 990, gain = 10%, CP =   X 990 = 900.

             And SP of 2nd fans = 990, loss = 10%,   CP  =    X 990 = 1100.

             Hence, CP of two fans =1100 + 900 = 2000.

            And  SP of two fans = 990 X2 = 1980. Since, CP > SP. It is loss.

            Loss = 2000 – 1980 = 20.  Hence, loss% =  X 100 = 1%.

 Q32.    ATQ, CP of sugar Rs. 4500.  => CP of  of sugar = 4500 X   = 1500

π    Gain at the rate of 10% = 1500 X10% = 150.

π    SP of rd of sugar  = 1500 + 150 = 1650.

π    Expected gain 12% of CP of sugar = 4500 X   = 540.

π    SP of sugar = 4500 + 540 = Rs. 5040.

π    SP of remaining sugar will be = 5040 – 1650 = Rs. 3390.

π    CP of remaining sugar will be = 4500 x   =    Rs. 3000.

Since, SP >CP. It is gain.  Gain = 3390 – 3000 = 390.

                        Hence, gain% =  X 100 = 13%.

 

   Q33.  ATQ,  Total CP = Rs. 96000, Total gain% = 10%,  Total SP = 96000 X  = 105600.

                              CP of  =  X 96000   = 38400.

π    SP of   =  X 38400  = 36096.

π    Remaining CP = 96000 – 38400 = 57600.

π    Remaining SP = 105600 – 36096 = 69504.

π    gain = SP –CP = 69504 – 57600 = Rs.11904. Hence, gain% =  X 100

π     %  =  20 %.

 

   Q34.    ATQ, CP of Shweta = Rs.1330 = SP of Alex .

                CP of Alex =   X 1330  = Rs.1400.

π    CP of Alex = SP of Vinod    (given)

π    CP of Vinod =   X 1400.  =          X 1400 = 1250.

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DISCOUNT

Q1.         ATQ,  Market Price = 4650, discount = 18%.

                Disc. = 18% of MP  =   X 4650 = 837

SINCE, SP = MP – disc.    =>  4650 – 837 = 3813.

Q2.         ATQ, MP= 960, SP = 816. Disc. = ?

                Disc. = 144      Hence,  disc.% =  X 100 = 15%.

Q3.         ATQ,  SP = 546, disc. = 104

Q4.         ATQ,      Disc. = 8%. SP =216.20, MP =?

                Let MP  = 100 Then,  Disc. = 100 X  = Rs. 8.

Since, SP is  92 then MP is 100.

                “      1    “       ‘           

               “    216.20 MP will be      X 216.20 = 235. 

Q5.         ATQ,  CP = 528, disc. = 12%, MP = ?

                                Let the MP be Rs. 100.  Disc = 100 x 12% = 12.   SP = 100 – 12 = 88.

                                If SP is 88     mp  =100

                                “    “       1      “       =  

                                “      “   528    “       =    X 528  =  600.

Q6.         Let CP = 100 CP  MP = 100 + 35 = 135

                                Disc. = 135 X 20% = 27.  SP = 135 – 27 = 108.  Now , SP > CP . It is gain.

                                Gain = 108 - 100 = 8   Hence, gain % = 8.

               

Q7.         Let CP = 100,  MP = 140  (100X 40%=40), Disc. =  30%.

                                Then SP = 140 - 140 X 30% = 140 – 42 =98.  Since, CP >SP it is loss.

Loss = 100 – 98 =2 Hence, loss% = 2%/

 

Q8.         ATQ, CP = 1080, gain = 25%. Then SO,  = 1350.  = 1350.

                                Let the MP be Rs.x . Then the disc. = 25% of x =   . Since, SP = MP – DISC.

                              X -    =  .  But, the SP = 1350. SO,  = 1350.  => x=   = 1800.

 

Q9.         Same as Q8. Hints:   X -    =  .  But, the SP = 13818. SO,  = 13818.= 16450.

 

Q10.       ATQ, CP = 1190, gain =20%.    SP =   X 1190 = 1428.

                Let the MP be Rs.x. disc. = 16% , SP = ?

                Then, disc. = x X  =  .  SO, SP= x -  = .  But, SP = 1428.

π     =1428  => x =  = 1700.

 

 Q11.      ATQ, CP =?, MP =?, Disc. =10%, Gain = 17%

                                Let MP be Rs.x,  disc. 10% then, x X  =   since, SP = MP – disc.

π    SP = X -   = .

Let CP = Rs.100. gain = 17%,  then SP = 117.

π     = 117  => x =   = 130. Hence, the MP is 30% above the CP.

 

 Q12.      ATQ, MP =?, CP =? ,  Disc. = 10%, Gain = 8%

                                Let CP = 100, gain =8, SP = CP + Gain = 108.

                                Let MP be Rs. x , Disc. = 10%  = x X   = .  SP = x -   =  .

π     =108   =>   x =   = 120. MP = 120.  Hence, 20% above the Cp should mark.

 

Q13.           ATQ, MP of TV = 18500, Disc.= 20% + 5%.

                                                MP of TV                                             =             18500

                                                1st  Disc. (20% of 18500)                 =    -           3700

                                                ______________________________________

                                                                                Remainder         =             14800

                                                2nd Disc. (5% of 14800)                   =    -             740

                                                ______________________________________

                                 Hence, the TV available on        =             14060.

 

 Q14.                      Let the MP = 100. 1st disc. 20% = 20 . then 100 – 20 = 80.

                                And 2nd disc. 5% on Rs. 80 = Rs. 4  then SP = 80 -4 =76.

                                Now, Disc. = MP – SP   => 100 – 76 = 24. Hence, 24%.

 

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Q5.      ATQ,  P = 20000, r = 12%.  

Then SI =  = 2400. For 2 yrs = 2400 X2 = 4800.

And P for 2nd yr= 20000 + 2400 = 22400

2nd yr Int. =  = 2688. 

Amount with SI = 20000 + 4800 = 24800.

Amount with CI = 22400 + 2688 = 25,088.

Gain after 2yrs = 25,088 -  24800 = Rs.288.

 

Q6.      ATQ,  P = 64000, t= 3yrs, r =  %.

            Int. on 1st yr =  =  = 4800. P for 2nd yr= 68800

            Int. on 2nd yr=   = 5160.  P for 3rd yr = 73960.

            Int. on 3nd yr=  = 5547. 

Hence, Maturity amount = 73960 + 5547 = Rs. 79507.

 

Q7.      ATQ, P = 6250, r= 8%/yrly,    and 4% half yearly.

                        Int. on 1st  half–yearly =   = 250.   P= 6250 + 250 = 6500.

                              Int. on 2nd  half–yearly =   = 260. Amount = 6500 + 260 = 6760.

                                 CI he gets = 6760 – 6250 = Rs. 510.

 

Q8.      ATQ,   P =16000, r = 10%yly,   and 5% half-yly.

                        Int. on 1st ½ yly    =    = 800. Amount = 16000 + 800= 16800.

                        Int. on 2nd ½ yly    =    = 840.  A =16800 + 840 = 17640.

                        Int. on 3rd ½ yly    =    = 882. Amount = 17640 + 882 = Rs.18522.        

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Q1.     P =6000, t = 2 yrs, r = 9%, CI =?

 

            A = Pn   = 60002  = 6000 X  X   = 7128.60.

               CI =A –P   = 7128.60 – 6000 =1128.60 .

 

Q4.      A = 102403        = 102403    = 102403  

            = 10240 X  X  X    = 1280 X  X   X 9 = Rs.14580.   CI = 4340.

 

Q6.      ATQ,  p=9000, t = 2yr 4m = 2 X  = 2  ,  r = 10%

               Since,  A= Pn   X     => A= 90002   X    

            =>A = 9000 X           X X    = Rs.11253.

 

Q7.      ATQ,   P = 8000, t= 2yrs,  r = 9%, and 10%

Since,     =

= 8000 x  X        = Rs. 9525.

 

Q8.                 = 125000 X X   = Rs.157464.

 

Q9.                    = 11000 X  X   = Rs.14641.

 

Q10.    18000 X (1 + ) X (1 + )  =  18000 X   X    = Rs. 22680.

 

Q12.    SI =  =  = 1200 X 2 = 2400.  A = 16000 + 2400 = Rs.18400.

            For 2nd yr P = 16000 + 1200 = Rs.17200.

            I =      = 1290 + 17200 = Rs.18490.  He gain = 18490 – 18400 =Rs.90.

 

Q15.    Let the sum be Rs. x,   SI =  = Rs.30.

            CI =    = 100 X  X  X   - 100

 =  - 100      =      =      Rs.33.1

            Diff. = CI – SI = 33.1 – 30 = 3.1

            If the diff is 3.1 then the sum is  Rs.100

            “         “          1           “          “            Rs.

            “          “       93           “          “          Rs.             X 93   = Rs. 3000.

Q18.    ATQ,    R = ?, P = 4000, A = 4410, t = 2years.

            4410 =       =>  =    =>  =  

=>    =  -1    =>R =   X 100 = 5%p.a.

 

Q21.    ATQ,   time = n=?, P = Rs.6250,  A = Rs.7290, R = 8%.

            7290 =     =>  =     =>   =  

 Hence, n = 2 years.

 

Q24.    ATQ,    Population = 120000, R =6% (increase)& 5% (decrease), n= 1.

            Population in 2010     = 120000 X   = Rs.127200.

            Population in 2011     = 127200 X   = Rs.120840.

 

Q25.    ATQ,  R = 2%, n = 2 hrs,

            Bacteria at the end of 2 hrs    = 500000 X  X

 

            = 200 X 51X 51 = 520200. Hence, the Bacteria at the end of 2 hrs = 520200.  

 

Q26.    Bacteria in 1st hr    = 200000 X  = 22000.

              

            Bacteria in 1st hr     = 22000 X  =19800.

 

Q27.    ATQ,   P =Rs. 625000, R = 8%, n= 2yrs. value=?

            Value of the machine    = 625000 X  X  = Rs.529000.

 

Q28.    Value after 3yrs     = 56000 X  X X    = Rs. 40824.

 

Q29.    Value of car after 1yr     = 348000 X   = Rs.313200.

                Value of car after 1yr     =  313200 X  = Rs.250560.

 

Q30.    ATQ, P. value (A)=Rs.291600, n=3yrs, dep. R = 10%. Purchased price (P)= ?.

            =>291600 =    => 291600 = P X  .

            => P =  = Rs. 400000. Hence the purchased value = Rs. 400000.

            ----------------------------------------------X-----------------------------------------------------

           

 

Q8.     R= 12 =  = %,  t = 2yrs p.a. , & half-yearly = 2n= 4 years.

         

               A =    = 65536 x    =Rs. 82944

          A =    =    =65536 x  

          = Rs. 83521.  He earn ; 83521 – 82944 =Rs. 577.

 

Q9.     Here, r quarterly = , t= 4n = 4/yly, for 6 month =  =2.

               A =    = 32000 X   = Rs. 32805.

 

Q10.   Here, r =        = 4% , t= 4n= 4.

          A =    = 390625 X   = Rs. 456976.

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