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ABHYAS PREP: RACES, DISCOUNTS, STOCKS AND HEIGHTS · TRUE DISCOUNT

True discount and present worth

Present worth is the sum that, put out at simple interest now, grows to the amount due. PW = 100A/(100 + RT) and true discount = A − PW, which is the simple interest on PW.

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Worked examples

Example 1 · level 1

Ananya has to pay ₹7,504 for a shipment of tea, due 1 year from now. Money is worth 12% per annum simple interest. What is the true discount?

  1. ₹804
  2. ₹900.48
  3. ₹1,023.27
  4. ₹6,700
Show solution
  1. R × T = 12.
  2. PW = 100 × 7,504/(100 + 12) = ₹6,700.
  3. TD = ₹7,504 − ₹6,700 = ₹804.
  4. Check: simple interest on ₹6,700 at 12% for 1 year = ₹804.

Answer: ₹804

Example 2 · level 2

Tenzin has to pay ₹6,136 for a load of steel rods, due 6 months from now. Money is worth 8% per annum simple interest. What is the true discount?

  1. ₹236
  2. ₹245.44
  3. ₹1,990.05
  4. ₹5,900
Show solution
  1. R × T = 4.
  2. PW = 100 × 6,136/(100 + 4) = ₹5,900.
  3. TD = ₹6,136 − ₹5,900 = ₹236.
  4. Check: simple interest on ₹5,900 at 8% for 6 months = ₹236.

Answer: ₹236

Example 3 · level 3

A trader in Mysuru owes a sum for a load of steel rods, due 18 months from now. At 10% per annum simple interest, the true discount on it is ₹2,595. What is the sum due?

  1. ₹4,036.67
  2. ₹14,705
  3. ₹17,300
  4. ₹19,895
Show solution
  1. R × T = 10 × 18/12 = 15.
  2. PW = TD × 100/(RT) = 2,595 × 100/15 = ₹17,300.
  3. Sum due = PW + TD = ₹17,300 + ₹2,595 = ₹19,895.

Answer: ₹19,895

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