ICSE Mathematics - 1998 sample paper

11/28/2011 CBSE




















Q1. A man invests Rs. 46,875
at 4% Per annum compound interest for 3 years. Calculate :


(i) The interest for the 1st year

(ii) The amount standing to his credit at the end of the 2nd years
.


(iii) The interest for the 3rd year.
Ans . (i)  P= Rs. 46,875

R=4% per annum

T= 1 year

A= 46,875 [ 1+   4/100  ]1

=46875 ( 104/100  )1



= Rs 48,750


C.I =48,750-46,875


=Rs. 1,875


(ii)


A=P [ 1+ R/100  ]N

= 46,875[ 1+ 4/100 ]2

= 46,875 x ( 104/100) x ( 104/100 )

=Rs. 50,700

C. I. = 50700 - 46875

= 3825


(iii)


A=P[ 1+ R/100]N

 = 46,875 [ 1+ 4/100  ]3

=46,875( 104/100 )3

= 46,875 x 1.12  = Rs 52500 Interest for third yr. means


C.I = 52,500- 46,875 = 5625 => Interest till
third yr- Interest till IInd year

= 5625-3825

=1800

 

Q2. A shopkeeper allowed a
discount of 20% on the marked price of an article, and sold it for  Rs. 896.
Calculate:

(i) His marked price ;


(ii)By selling the article at the
discounted price, if he still gains 12% on his cost price, what was the cost
price ?


(iii) What would have been his profit %,
if  he had sold the article at the marked price ?

Ans . Discount = 20%

Let M.P. = x


S.P.= Rs. 896

Discount = 20% of x

(i) M.P. = S.P.+ Discount

or

x = 896 + 20/100 x

= Rs. 1120



(ii) Gain = 12%

C.P. =   (S.P.x 100) / (100 + gain%) 

= (896 x100) / (100 + 12) =Rs. 800


(iii) When S.P.= M.P.

= 1120

=> ( 1120-800/800)100 = 320/8

=40%


& C.P.=Rs. 800


Gain % = [(S.P. x 100)/C.P.] - 100

= [(1075.2 x 100)/800]   - 100    =34.4 %



Q3. On a map drawn to a scale of 1 : 25000, a rectangular plot of land, ABCD,
has the following measurements, AB = 12cm & BC= 16cm . Angles A,B,C & D are
all 90o each. Calculate:


(i) The diagonal distance of the plot in km.


(ii) The area of the plot in sq. km .
Ans. Scale 1: 25000

AB= 12cm, BC= 16cm


After conversion


AB= 3km , BC= 4km


AC= Ö (AB2
+ BC2)
 


= 
Ö
(32+42)=5 km


Area= 3 x 4= 12 km2 


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