True Discount Questions

• Find the annual rate when TD and SI are given for the same sum: The true discount on a certain sum due 4 years hence is ₹ 75. The simple interest on the same sum for the same time and at the same rate is ₹ 225. Find the annual rate of interest.
• Inferring the annual interest rate from a credit sale gain: Vandana bought a watch for ₹ 600 and sold it the same day for ₹ 688.50 on 9 months’ credit. She states this way she “gained 2%.” Find the simple-interest rate per annum implicit in this credit sale.
• Present worth of two equal half-yearly instalments (assume simple interest at 10% p.a.): Find the present worth of Rs. 1404 due in two equal half-yearly instalments under simple interest at 10% per annum.
• Ready-money settlement of mutual dues at a true-discount rate: A owes B Rs. 456.75 payable 4 1/2 months hence; B owes A Rs. 455.51 payable 3 months hence. If they settle now at a true-discount rate of 4% per annum (simple), who pays whom and how much?
• Cash versus credit offer with simple interest (true discount) Kailash wants to sell his television. He has two offers: (A) ₹ 10,000 in cash today, or (B) ₹ 6,440 to be paid after 8 months on credit, when money is worth 18% per annum (simple interest). Which option gives Kailash the higher present worth?
• Early settlement of a future-dated payable using present worth Jagatram owes Mangalal ₹ 5,014 due 1 year from now. He wants to settle after 3 months from today. If the simple interest rate is 12% per annum, how much cash should Jagatram pay now to settle the account?
• Split payment versus single future payment (value at the same comparison point) Aarti must pay ₹ 440 to Babita after 1 year. Babita proposes: pay ₹ 220 now and defer ₹ 220 for 2 years. If simple interest is 10% per annum, does Aarti gain or lose under the new arrangement (relative to the original “after 1 year” schedule)?
• Mutual debts settled immediately using present worth M owes N ₹ 3,146 payable 1.5 years hence. N owes M ₹ 2,889 payable 6 months hence. If they settle accounts now at a simple interest rate of 14% per annum, who pays whom and how much?
• Compare three successive-discount offers: which gives the lowest net price? A company offers three alternative discount structures on the list price: (i) 25% then 15%, (ii) 30% then 10%, (iii) 35% then 5%. For a customer, which offer is best (i.e., yields the largest overall discount)?
• Compare single versus successive discounts on $500 Find the difference (in dollars) between: (A) a single 40% discount on $500, and (B) two successive discounts of 36% and 4% on $500.
• Equivalent single discount for three successive discounts What single discount is equivalent to successive discounts of 10%, 20%, and 30%?
• Bulk purchase discount from unit versus dozen pricing A single apple costs $25. A dozen apples cost $250. What is the approximate percentage discount when buying by the dozen compared to buying 12 singles?
• Recover marked price from difference between two discount schemes On a marked price M, the difference between the selling price with a single 30% discount and with two successive discounts of 20% and 10% is ₹ 72. Find the marked price M.
• Additional discount after initial markdown A fan lists at $1,500. It is first discounted by 20%. What additional single discount on the reduced price will bring the net price down to $1,104?
• Marked-up then discounted: determine overall gain or loss An article is marked 40% above cost price and then sold at a 30% discount on the marked price. What is the net percentage gain or loss relative to cost price?
• True discount on a short-term bill at simple interest Find the true discount on a bill of $1,260 due in 6 months at 10% per annum (simple interest).
• Present worth at compound interest Compute the present worth of $220.50 due in 2 years at 5% per annum compounded annually.
• True discount doubles when time doubles (same sum and rate) $21 is the true discount on $371 for a certain time at a certain rate. If the time is doubled at the same rate, what is the new true discount on $371?
• True discount for half the time (same sum and rate) $20 is the true discount on $260 due after a certain time. What will be the true discount on the same amount due after half of that time, at the same rate?
• The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit?