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A bill which being due at the end of 4 years is now worth $ 575, but if it is due in 2 years 6 months, it would now be worth $ 620. The sum of the bill is :
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- $ 695
- $ 725
- $ 713
- None of these
Correct Option: C
Let, the rate p.c. be r%.
Given :- Present worth = $ 575 and Time = 4 years
Let, $ x be the amount of the bill.
| ∴ Present worth = | Amount x Rate x Time |
| 100 + Rate x Time |
| Then, 575 = | 100 + 4r |
That is, 57500 + 2300r = 100x
∴ x = 575 + 23r …(1)
Present worth = $ 620 and Time = 2 years and 6 months = 2.5 years
| and 620 = | 100 + 2.5 r |
∴ 62000 + 1550r = 100x
∴ 6200 + 155r = 10x = 5750 + 230r [using (1)]
∴ 75r = 450
∴ r = 6
Putting the value of x in eq. (1) ⇒ x = 575 + 138 = $ 713.
Hence , The sum of the bill is $ 713.
