The following table shows the Expenditures of an Institution (in lakh ₹) per…
2020
The following table shows the Expenditures of an Institution (in lakh ₹) per annum:
The total amount of bonus paid by the institution during the given period is approximately what percent of the total amount of salary paid during this period?
Answer: D. ~ 1% — ConceptPercentage = (Part ÷ Base) × 100. When one quantity is expressed as a percent of another, the quantity being described is the part (numerator) and the…
- A.
~ 3%
- B.
~ 4%
- C.
~ 7%
- D.
~ 1%
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Show answer & explanation
Correct answer: D
Concept
Percentage = (Part ÷ Base) × 100. When one quantity is expressed as a percent of another, the quantity being described is the part (numerator) and the quantity it is measured against is the base (denominator).
For a year-wise table covering a period, the aggregates must be formed before dividing: add the part column over the whole period, add the base column over the same period, and only then take the ratio. Averaging the year-wise percentages, or using a single year's row, answers a different question.
The wording ‘total amount of bonus … is what percent of the total amount of salary’ therefore fixes the bonus column as the part and the salary column as the base, each summed across all five years.
Application
The two columns needed from the table, for 2015 to 2019 (amounts in ₹ lakh):
Year | Bonus | Salary of staff |
|---|---|---|
2015 | 3.00 | 288 |
2016 | 2.52 | 342 |
2017 | 3.84 | 324 |
2018 | 3.68 | 336 |
2019 | 3.96 | 420 |
Total | 17.00 | 1710 |
Total bonus over the period = 3.00 + 2.52 + 3.84 + 3.68 + 3.96 = 17.00 lakh.
Total salary over the period = 288 + 342 + 324 + 336 + 420 = 1710 lakh.
Required percentage = (17.00 ÷ 1710) × 100 = 1700 ÷ 1710.
1700 ÷ 1710 = 0.9942…, that is about 0.99 percent.
Rounded to the nearest value offered, the bonus total is approximately 1 percent of the salary total.
Cross-check and contrast
Work backwards to confirm: 1 percent of 1710 lakh is 17.1 lakh, and the actual bonus total is 17.00 lakh — a shade under 1 percent, which agrees with 0.99 percent.
The salary column is by far the largest expenditure head in the table, so dividing the bonus total by any other column's total instead would inflate the ratio to several times this size.
A single cell is not the answer either: the 2015 bonus entry is the number 3, which is an amount in ₹ lakh, not a percentage.
Averaging the five separate year-wise bonus-to-salary percentages (1.04, 0.74, 1.19, 1.10 and 0.94 percent) is a different calculation from dividing the totals; here it happens to land near 1 percent as well, but the question asks for the ratio of the totals.
Hence, over 2015 to 2019 the total bonus paid is approximately 1 percent of the total salary paid.