Arithmatical - True Discount

DIRECTIONS : Problems based on True discounts.
11. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is
  A.  Rs.1800
  B.  Rs.1450
  C.  Rs.1360
  D.  Rs.6800
Solution
Sum=S.I x T.D / S.I- T.D
= (85x80 / 85–80)
= Rs.1360.
12. The true discount on a bill due 9 months hence at 12% per annum is Rs.540. Find the amount of the bill and its present worth.
  A.  Rs.2500
  B.  Rs. 5000
  C.  Rs. 5500
  D.  Rs. 6000
Solution
Let amount be Rs.X then,
X×R×T/100+(R×T)=T.D
= X×12×3/4/100+(12×3/4)
= 540
X=(540×109/9)
= Rs. 6540
Amount= Rs. 6540.
P.W= Rs.(6540 - 540)
= Rs. 6000.
13. The true discount on a bill due 9 months hence at 16% per annum is Rs.189. The amount of the bill is
  A.  Rs.2268
  B.  Rs.1575
  C.  Rs.1764
  D.  Rs.1386
Solution
Let P.W. be x. Then, S.I. on Rs. x at 16% for 9 months = Rs. 189
Therefore x×16×9 / 12 × 1 / 100 = 189 or x = 1575
P.W = Rs.1575
Sum due = P.W. + T.D.
= Rs.(1575 + 189)
= Rs.1764.
14. A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other at a credit of Rs.12,880 to be paid after 8 months, money being at 18% per annum. Which is the best offer?
  A.  Rs.12,000 in cash
  B.  Rs.12880 ar credit
  C.  Both are equally good
  D.  None of these
Solution
P.W. of Rs. 12880 due 8 months hence= Rs. [12880×100 / 100 + (18 × 8 / 12)]
= Rs. (12880×100 / 112)
= Rs.11500
Clearly, Rs. 12000 in cash is a better offer.
Page 3 of 4 12 34