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BACK 1.A bill falls due in 1 year.The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years .By this arrangement he gains Rs.40.what is the amount of bill,if the money be worth 121/2%? sol: Let the amount be Rs.x If the bill falls due for 1 yr, Truediscount=(Amount*100)/(100+R*T) =(x*100)/(100+(25/2*1) If Accepting immediate payment of the half and to defer the payment of the other half for 2 years, Truediscount=(Amount*100)/(100+R*T) =[x/2+((x/2*100)/(100+(25/2*2))] x/2 for immediate payment, ((x/2*100)/(100+(25/2*2)) for paying after 2 yrs He gains Rs40 =>[x/2+((x/2*100)/(100+(25/2*2))] – (x*100)/(100+(25/2*1) = Rs40 => x/2+2x/5-8x/9=40 =>x=Rs.3600 Amount of the bill=Rs.3600 2.If the truediscount on a sum due 2yrs hence at 14% per annum be Rs168.The sum due is? Sol: Time=2yrs, Rate=14% Truediscount=Rs168,Amount=x TrueDiscount=(Amount*R*T)/(100+R*T) 168 =(x*14*2)/(100+(14*2)) =>x=Rs.768 3.The truediscount on Rs.2562 due 4 months hence is Rs.122.The rate % is? Sol: Amount=Rs.2562 Time=4/12yrs TrueDiscount=Rs122 Rate=X% TrueDiscount=(Amount*R*T)/(100+R*T) =>122=(2562*x*(4/12))/(100+(x*(4/12)) =>36600+122x=2562x =>Rate=15% 4.The Truediscount on Rs1760 due after a certain time at 12% per annum is Rs160The time after which it is due is: Sol: Amount=Rs.1760 Rate=12% Truediscount=Rs160 Time=x TrueDiscount=(Amount*R*T)/(100+R*T) =>x*11*12=100+12x =>x=5/6yr Time=10months 5.The interest on Rs.760 for 2yrs is the same as the Truediscount on Rs960 due 2yrs hence .If the rate of interest is same in both cases,it is sol: Principal=Rs.760 Time=2yrs amount=Rs960 P*T*R/100=(Amount*R*T)/(100+R*T) =>(750*2*r)/100=(960*r*2)/(100+2r) =>150r=2100 rate=14% 6.The SimpleInterest & TrueDiscount on a certain sum of money for a given time & at a given rate are Rs85 & Rs.80.The sum is............. sol: S.I= Rs.85 TrueDiscount=Rs80 Sum=(S.I.*TD)/(SI-T.D) =Rs.1360 7.A trader owes a maerchant Rs10028 due 1yr hence The trader wants to settle the account after 3 months .If the rate of interest is 12%per annum How much cash should he pay? Sol: Time=1yr but he settles account after 3months so time = 9months Cash to pay=(Amount*R*T)/(100+R*T) =(10028*100)/(100+12*(9/12)) =Rs.9200 8.A man buys a watch for Rs1950 in cash and sells it for Rs2200 at a credit of 1yrThe rate of interest is 10% per annum Then he gains / loose---------------amount? Sol: If he sells it for Rs2200 at a credit of 1yr then the present worth of that amount is Presentworth = (Amount*100) /(100+(R*T)) =(2200*100)/(100+10*1) =2000/- So he gains 2000-1950=Rs.50 9.A owes Rs.1573 payable 11/2yrs hence ,Aso B owes A Rs.144450 payabe 6months hence If they want to settle the accunt forth with ,keeping 14% as the rate of interest ,then who should pay & how much? Sol: B->A-----------Amount=Rs.1573 Rate=14% Time=3/2 Presentworth = (Amount*100) /(100+(R*T)) =(1573*100)/(100+(3/2)*14) =Rs1300 A->B------------Amount=Rs.1444.50 Rate=14% Time=1/2 Presentworth = (Amount*100) /(100+(R*T)) =(1444.50*100)/(100+(1/2)*14) =Rs1350 so B should pay Rs.1350 10.If Rs20 is the TrueDiscount on Rs260due after a certain time. What wil be trueDiscount on same sum due after ½ of former time, the rate of interest beng the same? Sol: Simple Interest on (260-20) for a gven time=Rs20 Simple Interest on (260-20) for a half time=Rs20*(1/2) =Rs10 True Discount on Rs.250=Rs10 True Discount on Rs.260=Rs10*260/250 =Rs10.40 11.A has to pay Rs.220 to B after 1yr.B asks A to pay Rs.110 in cash and defer the payment of Rs,.110 for 2 yrs.A agrees to it.If the rate of interest be 10% per annum in this mode of payment:... ............ sol: A has to pay =Present worth of Rs220 due 1yr hence =Rs.(220*100)/(100+(10*1)) =Rs.200 A actually pays=Rs.110+Presentworth of Rs110 due 2 yrs hence =[110+ (Amount*100) /(100+(R*T))] =[110+((110*100)/(100+(10*2)))] =Rs192.66 So A gains Rs(200-192.66)=Rs.7.34 BACK |