A firm is purchasing two items, both on credit on the same day. The credit term offered for the first item is 2 1/2 /10, 1/20, net 30; and the credit term offered for the second item is 3/5, 2/15, net 30. The declared purchase cost of item 1 is ₹ 60,000 and that of item 2 is ₹ 1,40,000. If both credits can be settled on the 14th day, what will be the total amount to be paid out ?

Correct — C, (c) ₹ 1,96,600.

Everything turns on reading the two credit terms, which are written in the standard commercial shorthand. A term of the form 'd/n' means a discount of d per cent if payment is made within n days, and 'net 30' means the whole invoice is due within thirty days.

ITEM 1 — terms '2 1/2 /10, 1/20, net 30' on a cost of ₹ 60,000. The first element is the MIXED NUMBER two-and-a-half, printed in the booklet as the digit 2 followed by a stacked fraction one-over-two, and then a solidus and 10. So the tiers are: 2½ per cent off if paid within 10 days; 1 per cent off if paid within 20 days; the whole amount due by day 30.

ITEM 2 — terms '3/5, 2/15, net 30' on a cost of ₹ 1,40,000: 3 per cent off if paid within 5 days; 2 per cent off if paid within 15 days; the whole amount due by day 30.

Both are settled on the SAME day, the fourteenth, and the fourteenth day falls in a DIFFERENT tier for each item. That is the trick of the question, and it is why two items are given rather than one.

ITEM 1 on day 14: past the 10-day window, but inside the 20-day window. So the SECOND tier applies, 1 per cent. 60,000 x 0·99 = 60,000 - 600 = ₹ 59,400 ITEM 2 on day 14: past the 5-day window, but inside the 15-day window. So the SECOND tier applies, 2 per cent. 1,40,000 x 0·98 = 1,40,000 - 2,800 = ₹ 1,37,200

TOTAL PAID = 59,400 + 1,37,200 = ₹ 1,96,600, which is option (c).

A useful check on the answer: the correct total is the LOWEST of the four options. Day 14 catches a discount tier on BOTH items, so every available error — missing a tier, applying only one item's discount, treating a payment as late — loses a discount and pushes the total UP. On a question of this shape the answer lies at the bottom of the range, and a candidate whose figure sits above the lowest option should suspect a missed tier rather than an arithmetic slip.

Note also what the spacing in the first term prevents. It is printed '2 1/2 /10', with the space kept, precisely so that the mixed number two-and-a-half is not read as the improper fraction twenty-one over two. Reading it as 10½ per cent would take ₹ 6,300 off the first item and produce a total of ₹ 1,90,900, which is not on the page at all. The 'th' of '14th' is a superscript in the booklet, money is set with the rupee sign followed by a space and Indian digit grouping, and the semicolon after 'net 30;' is as printed.

Why the others are wrong

• (a)₹ 1,97,200 — This is the only wrong option that comes out of a definite error, and the error is a precise one: it applies the 2 per cent discount to item 2 and NO discount at all to item 1. 2,00,000 - 2,800 = 1,97,200. That is what a candidate produces by reading item 1's terms as though they were simply '2½/10, net 30' and concluding that payment on day 14 is too late to earn anything. The middle tier, '1/20', is the piece that has been skipped, and it is easy to skip because the first term has three elements where the second has three as well but is set more plainly. Reading each term as a full LADDER of tiers, and locating the payment date on that ladder, is the whole discipline of the question.
• (b)₹ 1,97,500 — This figure corresponds to a discount of ₹ 2,500 on a gross of ₹ 2,00,000, and no combination of the printed tiers produces it. The discounts actually available are ₹ 1,500 or ₹ 600 on item 1, at 2½ and 1 per cent of 60,000, and ₹ 4,200 or ₹ 2,800 on item 2, at 3 and 2 per cent of 1,40,000. The possible totals from those are 5,700, 4,300, 4,800, 3,400, 1,500, 600, 4,200 and 2,800, and 2,500 is not among them. It is worth doing that enumeration in a question of this kind: where only a handful of discount combinations exist, an option that matches none of them can be discarded without further working.
• (d)₹ 1,98,400 — This implies a total discount of only ₹ 1,600, and like option (b) it corresponds to no combination of the printed tiers — the smallest single discount available is ₹ 600 and the next is ₹ 1,500, and no pair of available discounts sums to 1,600. It is the highest of the four options and therefore the smallest saving, which fits the general pattern of this option set: three of the four totals lie above the correct one, because every error in reading a credit term costs the buyer a discount rather than earning an extra one.

CREDIT TERMS are a piece of commercial vocabulary that appears in accounting, working-capital management and quantitative aptitude alike, and the notation is compact.

'd/n' — a cash discount of d per cent for payment within n days. 'net N' — the full invoice amount is payable within N days. Several discount tiers may be stacked: '3/5, 2/15, net 30' offers 3 per cent within five days, 2 per cent within fifteen, and the whole sum within thirty.

THE METHOD for any such problem has three steps. ONE — expand each term into its full ladder of tiers with the day ranges attached. TWO — place the payment date on the ladder, taking the BEST tier whose window has not yet closed. A payment on day 14 under '3/5, 2/15, net 30' earns 2 per cent, not 3, because the five-day window has passed, and not zero, because the fifteen-day window has not. THREE — apply the tier to that item's own invoice value, and only then add across items.

THE ECONOMICS OF A CASH DISCOUNT is what makes the topic more than arithmetic. Offering 2 per cent for payment twenty days early is expensive: the seller is paying 2 per cent of the invoice for twenty days of money, which annualises to a very large rate. Sellers offer such discounts because they shorten the collection period, reduce the working capital tied up in receivables and reduce the risk of default; buyers take them when their own cost of funds is lower than the implied rate. The standard way to compare is to convert the discount into an annual equivalent — the discount rate divided by the amount actually paid, scaled by the number of such periods in a year.

WHY THE QUESTION USES TWO ITEMS with DIFFERENT terms settled on the SAME day is the design point. A single item would test only whether the notation is understood. Two items whose tier boundaries fall on either side of day 14 test whether the candidate re-evaluates the date against each ladder separately instead of deciding once that the payment is 'in the middle tier' and applying the same conclusion twice. Here it happens that both items do land in their second tier, but they do so for different reasons and against different day ranges.

Key facts

• In credit terms, 'd/n' means a discount of d per cent for payment within n days, and 'net N' means the full amount is due within N days.
• '2 1/2 /10, 1/20, net 30' means 2½ per cent within 10 days, 1 per cent within 20 days, and the whole amount by day 30.
• '3/5, 2/15, net 30' means 3 per cent within 5 days, 2 per cent within 15 days, and the whole amount by day 30.
• A payment on day 14 takes the best tier whose window is still open: 1 per cent on the first item and 2 per cent on the second.
• 60,000 less 1 per cent is 59,400; 1,40,000 less 2 per cent is 1,37,200; the total is 1,96,600.
• Every misreading of a credit term costs the buyer a discount, so the correct total is the lowest of the four options.
• Reading '2 1/2' as the improper fraction twenty-one over two would give a 10½ per cent discount and a total of 1,90,900, which is not among the options — the printed spacing exists to prevent that reading.
• A cash discount is expensive for the seller relative to the days saved, and is offered to shorten the collection period and reduce receivables and default risk.

Common traps

• Missing a middle tier. Item 1 has three elements, and reading it as '2½/10, net 30' loses the 1 per cent that day 14 actually earns.
• Applying one item's tier decision to the other. Each term must be re-read against the payment date separately, because the day ranges differ.
• Reading '2 1/2' as twenty-one over two. The printed spacing separates the whole number from the fraction, and a 10½ per cent discount produces a total that is not on the page.
• Applying a discount to the combined invoice value. Each discount belongs to its own item's cost and the totals are added only at the end.

• practice — not a real PYQ

  An invoice for 80,000 rupees carries credit terms of 2/10, 1/20, net 45. If it is settled on the 18th day, the amount payable is

  • (a)78,400 rupees
  • (b)79,200 rupees
  • (c)80,000 rupees
  • (d)78,000 rupees

  Answer(b) 79,200 rupees — day 18 is past the ten-day window but within the twenty-day window, so the 1 per cent tier applies: 80,000 less 800 is 79,200. Taking the 2 per cent tier would give 78,400 and treating the payment as too late for any discount would give 80,000, and both are the standard errors on this form of question.

• practice — not a real PYQ

  Credit terms of '3/10, net 30' mean that

  • (a)3 per cent interest is charged if payment is delayed beyond 10 days
  • (b)a 3 per cent discount is allowed for payment within 10 days, with the full amount due in 30 days
  • (c)3 per cent of the invoice must be paid within 10 days and the rest in 30
  • (d)the invoice is payable in 3 instalments over 10 days

  Answer(b) a 3 per cent discount is allowed for payment within 10 days, with the full amount due in 30 days — the notation d/n always names a discount and the window in which it can be earned, and 'net N' names the day by which the whole invoice must be settled. It is a discount for paying early, not a charge levied for paying late.