Arithmatical - True Discount

DIRECTIONS : Problems based on True discounts.
15. The true discount on a certain sum of money due 3 years hence is Rs.250 and the simple interest on the same sum for the time and at the same rate is Rs.375. Find the sum?
  A.  Rs.500
  B.  Rs.750
  C.  Rs.1000
  D.  Rs.1250
Solution
T.D= Rs.250
S.I= Rs.375
Sum due= S.I×T.D/(S.I)-(T.D)
= Rs.(375×250/375-250 )
= Rs.750.
16. The interest on Rs.750 for 2 years is the same as the true discount on Rs.960 due 2 years hence. If the rate of interest is the same in both cases, it is
  A.  10%
  B.  12%
  C.  14%
  D.  18%
Solution
S.I. on Rs.750 = T.D. on Rs.960
This means P.W. of Rs.960 due 2 years hence is Rs.750.
Therefore T.D.= Rs.(960 - 750)
= Rs.210.
Thus, S.I. on Rs.750 for 2 years is Rs.210
Rate= Rs.(100 × 210 / 750 × 2)%
= 14%.
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