Distributing a Stationery Budget with a Rounding Remainder
You are closing the monthly stationery return for a unit office. The officer has approved Rs 76,000 for five sections, A to E, in the ratio 5:4:3:2:1. The accounting software accepts only whole rupees and rejects any return whose five allocations do not add exactly to Rs 76,000. A colleague proposes giving any leftover rupees to Section A because it is the largest and “can absorb them”. Section B has already spent Rs 21,000. Section C has returned Rs 1,200 as unspent. The audit cell requires a written rounding rule and a note on any section that exceeds its allocation by more than 2 per cent. You must submit the return today; there is no time to reopen the budget. The section strength is A 45, B 36, C 27, D 18 and E 9, but the budget ratio was fixed by the officer and is not based on strength.
1. Calculate the exact share of each section and convert it into whole rupees so that the total is exactly Rs 76,000. Show your rounding method.
Read the worked answer
The ratio 5:4:3:2:1 has 15 parts, so one part is 76,000 ÷ 15 = Rs 5,066.666… Exact shares:
| Section | Ratio | Exact share | Floor | Fraction | Whole-rupee allocation |
|---|---|---|---|---|---|
| A | 5 | 25,333.33 | 25,333 | .33 | 25,333 |
| B | 4 | 20,266.67 | 20,266 | .67 | 20,267 |
| C | 3 | 15,200.00 | 15,200 | .00 | 15,200 |
| D | 2 | 10,133.33 | 10,133 | .33 | 10,133 |
| E | 1 | 5,066.67 | 5,066 | .67 | 5,067 |
| Total | 15 | 76,000 | 75,998 | 76,000 |
The floor values total Rs 75,998, leaving Rs 2. Under the largest-remainder method, the two rupees go to the sections with the largest fractions: B and E, both .67. The result adds exactly to Rs 76,000 and keeps every section within one rupee of its exact share.
2. Section B has spent Rs 21,000. Calculate its percentage of allocation and decide whether the audit cell must be informed.
Read the worked answer
Section B’s allocation is Rs 20,267. The excess is 21,000 − 20,267 = Rs 733. As a percentage of allocation: 733 ÷ 20,267 × 100 = 3.62 per cent (using the exact share of 20,266.67 gives 733.33 ÷ 20,266.67 = 3.62 per cent, so rounding does not change the conclusion). The audit threshold is “more than 2 per cent,” and 3.62 per cent exceeds it. The audit cell must therefore be informed, with the amount of the excess and the reason for it. The return should not hide the overrun by reducing another section’s allocation or by treating the Rs 1,200 returned by Section C as an automatic top-up for B. Any re-appropriation needs the officer’s approval and a separate entry.
3. Evaluate the colleague’s proposal to give leftover rupees to Section A. State the rounding rule you would write on the return and explain how Section C’s Rs 1,200 return should be treated.
Read the worked answer
The proposal is not acceptable. Giving both leftover rupees to A produces A = 25,335, while B and E stay at their floor values. That is not the largest-remainder result, it rewards the largest section for being largest, and it cannot be defended if the audit cell recomputes the ratio. A clerk’s rounding rule should be written on the return, for example: “Exact shares calculated to two decimal places; whole-rupee allocations assigned by taking the floor and distributing the remaining rupees to the largest fractional remainders; ties broken by section order.” Section C’s Rs 1,200 is an unspent balance, not a surplus that B may automatically absorb. It should be shown as returned to the budget head, and any transfer to cover B’s overrun must be approved and recorded separately. The return should show C’s allocation, expenditure of Rs 14,000 and the Rs 1,200 return.