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
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
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