You owe Rs 6,600 in two years. What lump sum clears the debt today? That fair sum is the present worth . The gap is the true discount .
Read the Article: True Discount: Formulas, Shortcuts and Solved Examples →
0 / 25 correct · click an option to check it · +0 pts today
Q1. If S.I. is the simple interest and T.D. is the true discount on the same sum for the same time and rate, what is the correct formula for the sum?
Show answer and explanation
Answer: A
On the same sum, time, and rate, True Discount (T.D.) is interest on the Present Worth. Simple Interest (S.I.) is interest on the full Amount. Since Amount is always more than Present Worth, S.I. is always more than T.D. Solving these two relations together gives the identity: Sum = (S.I. x T.D.) / (S.I. – T.D.).
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q2. What is the correct formula for the present worth (P.W.) of an amount A due in T years at R% per annum simple interest?
Show answer and explanation
Answer: C
Present Worth (P.W.) is the sum which, if invested now, would grow to the Amount A. This growth happens at the given rate R, over the given time T. True Discount is simple interest on P.W.: T.D. = (P.W. x R x T) / 100. Since A = P.W. + T.D., substituting and solving for P.W. gives the formula. P.W. = (100 x A) / (100 + R x T). Here R is the rate percent per annum, and T is the time in years.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q3. True discount is defined as simple interest on which amount?
Show answer and explanation
Answer: A
True Discount (T.D.) is not interest on the Amount due. It is interest on a smaller sum. That smaller sum is called the Present Worth (P.W.). P.W. is the amount that would grow to the Amount due, if invested now. So T.D. is exactly the simple interest earned on the Present Worth. This interest is calculated over the given time, at the given rate.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q4. What is the correct relationship between the amount due, its present worth, and the true discount?
Show answer and explanation
Answer: B
When money is due later, its present worth (P.W.) is the sum that would grow to the Amount if invested now. The difference between the Amount and the Present Worth is the True Discount (T.D.). T.D. is the benefit of paying the sum early. So the Amount due equals the Present Worth plus the True Discount: Amount = P.W. + T.D.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q5. The true discount on a sum of Rs 2700 due after some years at 4% per annum is Rs 450. In how many years is the sum due?
Show answer and explanation
Answer: C
The sum (amount) due is Rs 2700. The true discount is T.D. = Rs 450. The rate is R = 4% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 2700 – 450 = Rs 2250. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 450 = 45000. The denominator is 2250 x 4 = 9000. So Time = 45000 / 9000 = 5 years. Check: T.D. = (P.W. x R x T) / 100 = (2250 x 4 x 5) / 100 = 450.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q6. The true discount on a sum of Rs 5208 due after some years at 6% per annum is Rs 1008. In how many years is the sum due?
Show answer and explanation
Answer: D
The sum (amount) due is Rs 5208. The true discount is T.D. = Rs 1008. The rate is R = 6% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 5208 – 1008 = Rs 4200. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 1008 = 100800. The denominator is 4200 x 6 = 25200. So Time = 100800 / 25200 = 4 years. Check: T.D. = (P.W. x R x T) / 100 = (4200 x 6 x 4) / 100 = 1008.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q7. The true discount on a sum of Rs 5520 due after some years at 15% per annum is Rs 2070. In how many years is the sum due?
Show answer and explanation
Answer: B
The sum (amount) due is Rs 5520. The true discount is T.D. = Rs 2070. The rate is R = 15% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 5520 – 2070 = Rs 3450. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 2070 = 207000. The denominator is 3450 x 15 = 51750. So Time = 207000 / 51750 = 4 years. Check: T.D. = (P.W. x R x T) / 100 = (3450 x 15 x 4) / 100 = 2070.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q8. The true discount on a sum of Rs 160 due after some years at 12% per annum is Rs 60. In how many years is the sum due?
Show answer and explanation
Answer: D
The sum (amount) due is Rs 160. The true discount is T.D. = Rs 60. The rate is R = 12% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 160 – 60 = Rs 100. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 60 = 6000. The denominator is 100 x 12 = 1200. So Time = 6000 / 1200 = 5 years. Check: T.D. = (P.W. x R x T) / 100 = (100 x 12 x 5) / 100 = 60.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q9. The true discount on a sum of Rs 10050 due after some years at 10% per annum is Rs 3350. In how many years is the sum due?
Show answer and explanation
Answer: A
The sum (amount) due is Rs 10050. The true discount is T.D. = Rs 3350. The rate is R = 10% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 10050 – 3350 = Rs 6700. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 3350 = 335000. The denominator is 6700 x 10 = 67000. So Time = 335000 / 67000 = 5 years. Check: T.D. = (P.W. x R x T) / 100 = (6700 x 10 x 5) / 100 = 3350.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q10. The true discount on a sum of Rs 4620 due after some years at 8% per annum is Rs 1320. In how many years is the sum due?
Show answer and explanation
Answer: C
The sum (amount) due is Rs 4620. The true discount is T.D. = Rs 1320. The rate is R = 8% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 4620 – 1320 = Rs 3300. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 1320 = 132000. The denominator is 3300 x 8 = 26400. So Time = 132000 / 26400 = 5 years. Check: T.D. = (P.W. x R x T) / 100 = (3300 x 8 x 5) / 100 = 1320.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q11. The true discount on a sum of Rs 7975 due after some years at 5% per annum is Rs 725. In how many years is the sum due?
Show answer and explanation
Answer: B
The sum (amount) due is Rs 7975. The true discount is T.D. = Rs 725. The rate is R = 5% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 7975 – 725 = Rs 7250. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 725 = 72500. The denominator is 7250 x 5 = 36250. So Time = 72500 / 36250 = 2 years. Check: T.D. = (P.W. x R x T) / 100 = (7250 x 5 x 2) / 100 = 725.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q12. The true discount on a sum of Rs 9270 due after some years at 20% per annum is Rs 4120. In how many years is the sum due?
Show answer and explanation
Answer: A
The sum (amount) due is Rs 9270. The true discount is T.D. = Rs 4120. The rate is R = 20% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 9270 – 4120 = Rs 5150. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 4120 = 412000. The denominator is 5150 x 20 = 103000. So Time = 412000 / 103000 = 4 years. Check: T.D. = (P.W. x R x T) / 100 = (5150 x 20 x 4) / 100 = 4120.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q13. The true discount on a sum of Rs 1219 due after some years at 6% per annum is Rs 69. In how many years is the sum due?
Show answer and explanation
Answer: D
The sum (amount) due is Rs 1219. The true discount is T.D. = Rs 69. The rate is R = 6% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 1219 – 69 = Rs 1150. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 69 = 6900. The denominator is 1150 x 6 = 6900. So Time = 6900 / 6900 = 1 year. Check: T.D. = (P.W. x R x T) / 100 = (1150 x 6 x 1) / 100 = 69.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q14. The true discount on a sum of Rs 9870 due after some years at 8% per annum is Rs 2820. In how many years is the sum due?
Show answer and explanation
Answer: C
The sum (amount) due is Rs 9870. The true discount is T.D. = Rs 2820. The rate is R = 8% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 9870 – 2820 = Rs 7050. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 2820 = 282000. The denominator is 7050 x 8 = 56400. So Time = 282000 / 56400 = 5 years. Check: T.D. = (P.W. x R x T) / 100 = (7050 x 8 x 5) / 100 = 2820.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q15. The true discount on a sum of Rs 280 due after some years at 12% per annum is Rs 30. In how many years is the sum due?
Show answer and explanation
Answer: B
The sum (amount) due is Rs 280. The true discount is T.D. = Rs 30. The rate is R = 12% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 280 – 30 = Rs 250. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 30 = 3000. The denominator is 250 x 12 = 3000. So Time = 3000 / 3000 = 1 year. Check: T.D. = (P.W. x R x T) / 100 = (250 x 12 x 1) / 100 = 30.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q16. The true discount on a sum of Rs 2000 due after some years at 5% per annum is Rs 400. In how many years is the sum due?
Show answer and explanation
Answer: D
The sum (amount) due is Rs 2000. The true discount is T.D. = Rs 400. The rate is R = 5% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 2000 – 400 = Rs 1600. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 400 = 40000. The denominator is 1600 x 5 = 8000. So Time = 40000 / 8000 = 5 years. Check: T.D. = (P.W. x R x T) / 100 = (1600 x 5 x 5) / 100 = 400.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q17. The true discount on a sum of Rs 10240 due after some years at 12% per annum is Rs 3840. In how many years is the sum due?
Show answer and explanation
Answer: C
The sum (amount) due is Rs 10240. The true discount is T.D. = Rs 3840. The rate is R = 12% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 10240 – 3840 = Rs 6400. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 3840 = 384000. The denominator is 6400 x 12 = 76800. So Time = 384000 / 76800 = 5 years. Check: T.D. = (P.W. x R x T) / 100 = (6400 x 12 x 5) / 100 = 3840.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q18. The true discount on a sum of Rs 7440 due after some years at 6% per annum is Rs 1440. In how many years is the sum due?
Show answer and explanation
Answer: A
The sum (amount) due is Rs 7440. The true discount is T.D. = Rs 1440. The rate is R = 6% per year. True Discount is the simple interest earned on the Present Worth (P.W.) over the unknown time. First find P.W.: P.W. = Amount – T.D. = 7440 – 1440 = Rs 6000. The time formula is Time = (100 x T.D.) / (P.W. x R). The numerator is 100 x 1440 = 144000. The denominator is 6000 x 6 = 36000. So Time = 144000 / 36000 = 4 years. Check: T.D. = (P.W. x R x T) / 100 = (6000 x 6 x 4) / 100 = 1440.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q19. The true discount on a sum of Rs 8680 due 2 years hence is Rs 1680. Find the rate percent per annum.
Show answer and explanation
Answer: C
The sum (amount) due is Rs 8680. The true discount is T.D. = Rs 1680. The time is T = 2 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 8680 – 1680 = Rs 7000. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 1680 = 168000. The denominator is 7000 x 2 = 14000. So Rate = 168000 / 14000 = 12%. Check: T.D. = (P.W. x R x T) / 100 = (7000 x 12 x 2) / 100 = 1680.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q20. The true discount on a sum of Rs 2542 due 3 years hence is Rs 492. Find the rate percent per annum.
Show answer and explanation
Answer: B
The sum (amount) due is Rs 2542. The true discount is T.D. = Rs 492. The time is T = 3 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 2542 – 492 = Rs 2050. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 492 = 49200. The denominator is 2050 x 3 = 6150. So Rate = 49200 / 6150 = 8%. Check: T.D. = (P.W. x R x T) / 100 = (2050 x 8 x 3) / 100 = 492.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q21. The true discount on a sum of Rs 3224 due 2 years hence is Rs 624. Find the rate percent per annum.
Show answer and explanation
Answer: A
The sum (amount) due is Rs 3224. The true discount is T.D. = Rs 624. The time is T = 2 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 3224 – 624 = Rs 2600. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 624 = 62400. The denominator is 2600 x 2 = 5200. So Rate = 62400 / 5200 = 12%. Check: T.D. = (P.W. x R x T) / 100 = (2600 x 12 x 2) / 100 = 624.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q22. The true discount on a sum of Rs 7896 due 3 years hence is Rs 846. Find the rate percent per annum.
Show answer and explanation
Answer: D
The sum (amount) due is Rs 7896. The true discount is T.D. = Rs 846. The time is T = 3 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 7896 – 846 = Rs 7050. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 846 = 84600. The denominator is 7050 x 3 = 21150. So Rate = 84600 / 21150 = 4%. Check: T.D. = (P.W. x R x T) / 100 = (7050 x 4 x 3) / 100 = 846.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q23. The true discount on a sum of Rs 3108 due 3 years hence is Rs 1008. Find the rate percent per annum.
Show answer and explanation
Answer: D
The sum (amount) due is Rs 3108. The true discount is T.D. = Rs 1008. The time is T = 3 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 3108 – 1008 = Rs 2100. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 1008 = 100800. The denominator is 2100 x 3 = 6300. So Rate = 100800 / 6300 = 16%. Check: T.D. = (P.W. x R x T) / 100 = (2100 x 16 x 3) / 100 = 1008.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q24. The true discount on a sum of Rs 2900 due 2 years hence is Rs 400. Find the rate percent per annum.
Show answer and explanation
Answer: C
The sum (amount) due is Rs 2900. The true discount is T.D. = Rs 400. The time is T = 2 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 2900 – 400 = Rs 2500. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 400 = 40000. The denominator is 2500 x 2 = 5000. So Rate = 40000 / 5000 = 8%. Check: T.D. = (P.W. x R x T) / 100 = (2500 x 8 x 2) / 100 = 400.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples
Q25. The true discount on a sum of Rs 4590 due 4 years hence is Rs 2040. Find the rate percent per annum.
Show answer and explanation
Answer: A
The sum (amount) due is Rs 4590. The true discount is T.D. = Rs 2040. The time is T = 4 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 4590 – 2040 = Rs 2550. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 2040 = 204000. The denominator is 2550 x 4 = 10200. So Rate = 204000 / 10200 = 20%. Check: T.D. = (P.W. x R x T) / 100 = (2550 x 20 x 4) / 100 = 2040.
Related topics: True Discount: Formulas, Shortcuts and Solved Examples