## 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