# XAT 2015 Quant & DI Q13: Percentage

This question appeared as a part of the quantitative reasoning and data interpretation section of the XAT 2015. A total of 33 questions appeared in this section in XAT 2015. This one is a __hard__ aptitude question and tests the concept in percent, finding highest and lowest value and range based on data regarding tax slabs. Question 13 of 33 questions that appeared in this section in XAT 2015.

## Question

The taxes for various income slabs are given below:

Income Slab (I) | Tax rate |
---|---|

I ≤ 500 | 0 |

500 < I ≤ 2000 | 5% |

2000 < I ≤ 5000 | 10% |

5000 < I < 10,000 | 15% |

There are 15 persons working in an organization. Out of them 3 to 5 persons are falling in each of the income slabs mentioned above. Which of the following is the correct tax range of the 15 person? (e.g., If one is earning Rs. 2000, the tax should be : 500 * 0 + 1500 * 0.05)

- 1350 to 7350, both excluded
- 1350 to 9800, both included
- 2175 to 7350, both excluded
- 2175 to 9800, both included
- None of the above

** Correct Answer** Choice A. The range as 1350 to 7350, both excluded.

## Explanatory Answer

### Given Data

3 to 5 persons in the organization can fall under each income slab.

### Approach

To find the range of the of tax paid by all 15 persons, we will have to break the task into the following steps

- Find minimum possible tax that has to be paid by anyone for each income slab.
- Find maximum possible tax that has to be paid by anyone for each income slab.
- Divide 15 people with least number of employees in the high income slab and maximum number of employees in the low income slab and pick the low end of the range for each slab to compute the lowest tax payable by all 15.
- Divide 15 people with least number of employees in the low income slab and maximum number of employees in the high income slab and pick the high end of the range for each slab to compute the maximum tax payable by all 15.

#### Steps 1 & 2: Find minimum and maximum possible tax that has to be paid by anyone for each income slab.

Tax is calculated as follows: If one is earning Rs. 2000, the tax should be: 500 * 0 + 1500 * 0.05

# Income Slabs

- Tax Rate
- Minimum Income
- Maximum Income
- Minimum Tax
- Maximum Tax

# I ≤ 500

- Nil
- 0
- 500
- 0
- 0

# 500 < I ≤ 2000

- 5%
- 501
- 2000
- Nil for Rs.500 1 * 0.05 = 0.05
- Nil for Rs.500 0 + 1500 * 0.05 = 75

(A)

# 2000 < I ≤ 5000

- 10%
- 2001
- 5000
- Tax for Rs.2000 = 75 (A) On next Rs.1: 1 * 0.10 = 0.10

Total tax = 75 + 0.1 = 75.1 - Tax for Rs.2000 = 75 (A) Next 3000: 3000 * 0.1 = 300

Total tax = 75 + 300 = 375 (B)

# 2000 < I < 5000

- 15%
- 5001
- 9999
- Tax for Rs.5000 = 375 (B) On next Rs.1: 1 * 0.15 = 0.15

Total tax = 375 + 0.15 = 375.15 - Tax for Rs.5000 = 375 (B) Next 4999: 4999 * 0.15 = 749.85

Total = B + 749.85 = 1124.85

#### Step 3: Compute the minimum tax that all 15 persons will pay

Total tax paid by all 15 will be minimum when more people are in the lower income slab and they also pay the minimum tax in that slab. We need to keep in mind that __3 to 5 people are in each income slab__.

Then the number of person under each income tax for this to be possible is as follows

# Income Slabs

- Number of Persons
- Minimum Tax
- Tax Paid = Number of persons * Minimum tax

# I ≤ 500

- 5
- Rs.0
- 5 * 00

# 500 < I ≤ 2000

- 4
- Rs.0.05
- 4 * 0.050.20

# 2000 < I ≤ 5000

- 3
- Rs.75.1
- 3 * 75.1225.3

# 5000 < I < 10000

- 3
- Rs.375.1
- 3 * 375.11125.45

The lowest value of the range is Rs.(0 + 0.20 + 225.3 + 125.45) = 1350.95, which is above 1350.

#### Step 4: Compute the maximum tax that all 15 persons will pay

The tax paid by all 15 will be maximum when more people are in the higher income slab and they pay the maximum tax in that slab.

Then the number of person under each income tax for this to be possible is as follows

# Income Slabs

- Number of Persons
- Maximum Tax
- Tax Paid = Number of persons * Maximum tax

# I ≤ 500

- 3
- Rs.0
- 3 * 00

# 500 < I ≤ 2000

- 3
- Rs.75
- 3 * 75225

# 2000 < I ≤ 5000

- 4
- Rs.375
- 4 * 3751500

# 5000 < I < 10000

- 5
- Rs.1124.85
- 5 * 1124.855624.25

Thus the upper value of the range is (0 + 225 + 1500 + 5624.25) = 7349 which is below 7350.

Combining both the upper and lower value we get the range as 1350 to 7350, both excluded.

The correct answer is Choice A.

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