More Questions Based On True Discount

1.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

2.If Rs.10 be allowed as truedscount on a bill of Rs.110 at the end of a certaimn time ,then discount allowed on the same sum due at the end of double the time.
sol:
Amount=Rs110
TrueDiscount=Rs10
Present worth=Amount-TrueDiscount
=Rs110-10
=Rs.100
SI on Rs.100 for a certain time =Rs.10
SI on Rs.100 for doube the time =Rs.20
TrueDiscount on (100+20)=120-100
=Rs20
TrueDiscount on Rs.110 =(110*20)/120
=Rs18.33

3.A man wants to se hs scooter .There are two offers one at Rs12000 cash and other at acredit of Rs12880 to be paid after 8 months ,money being at 18% per annum which is better offer?
Sol:
offer1=Rs12000
offer2 Present worth= (Amount*100) /(100+(R*T))

=Rs.12880*100/(100+(18*(8/12))
=Rs11,500
The first offer is better as if he gains 500/-
if he sells at Rs.12000 is better

4.Goods were bought for Rs.600 and sold the same day for Rs.688.80 at a credit of 9 months and thus gaining 2% rate of interest per annum is ?
sol:
Method I:
Amount=Rs.688.50
Time=9.12
Gaining 2%----------->Presentworth=102%of 600=(102*600)/100
=Rs.612
Presentworth=(Amount*100)/(100+(T*R))
612=(688.80*100)/(100+((9/2)*R))
=>R=162/3%
Method II:
TrueDiscount=688.50-612
=Rs.76.50
Rate=TrueDiscount*100/(P.W*T)
=(76.50*100)/(612*(9/12))
=162/3%

5.The present worth of Rs.1404 due in 2 equal half yearly installments at 8% per annu8m S.I is ?
SOl:
Presentworth=(Amount*100)/(100+(T*R))
PresentWorth=Presentworth of Rs.702 6 months hence +
Presentworth of Rs.702 1yr hence
= (702*100)/(100+(1/2*8)) + (702t*100)/(100+(1*8))
=Rs.1325