UPSC CBI DSP LDCE Archives

31. A shopkeeper fixes the marked price of an item 25% above its cost pric

A shopkeeper fixes the marked price of an item 25% above its cost price. What percentage of discount may be allowed to gain 6%?

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15.5%

15.2%

15.0%

15.8%

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Let the Cost Price (CP) of the item be ₹ 100.
The shopkeeper fixes the Marked Price (MP) 25% above the cost price.
MP = CP + 25% of CP = 100 + (25/100) * 100 = 100 + 25 = ₹ 125.
The desired gain is 6%. The Selling Price (SP) must be CP plus the gain.
SP = CP + 6% of CP = 100 + (6/100) * 100 = 100 + 6 = ₹ 106.
The discount is the difference between the Marked Price and the Selling Price.
Discount = MP – SP = 125 – 106 = ₹ 19.
The discount percentage is calculated on the Marked Price.
Discount Percentage = (Discount / MP) * 100% = (19 / 125) * 100%.
(19 / 125) * 100 = (19 * 4 / 125 * 4) * 100 = (76 / 500) * 100 = 76 / 5 = 15.2%.

Profit percentage is calculated on Cost Price, while Discount percentage is calculated on Marked Price.

This type of problem involves the relationship between Cost Price, Marked Price, Selling Price, Profit/Loss percentage, and Discount percentage. The Marked Price is typically set above the Cost Price, and the discount is offered on the Marked Price to arrive at the Selling Price.

32. A man buys a cycle for ₹ 1,400 and sells it at a loss of 15%. What is

A man buys a cycle for ₹ 1,400 and sells it at a loss of 15%. What is the selling price of the cycle?

₹ 1,190

₹ 1,160

₹ 210

₹ 1,180

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The cost price (CP) of the cycle is ₹ 1,400.
The cycle is sold at a loss of 15%.
The amount of loss is 15% of the cost price.
Loss amount = 15% of ₹ 1,400 = (15/100) * 1400 = 15 * 14 = ₹ 210.
The selling price (SP) is the cost price minus the loss.
SP = CP – Loss amount = ₹ 1,400 – ₹ 210 = ₹ 1,190.
Alternatively, the selling price can be calculated directly as CP * (1 – Loss%/100).
SP = 1400 * (1 – 15/100) = 1400 * (85/100) = 14 * 85 = ₹ 1,190.

Loss is calculated as a percentage of the cost price. Selling price in case of loss is Cost Price minus Loss amount.

Profit or loss percentages are typically calculated on the cost price unless otherwise stated.

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33. In 2020, the medical expense of a person increased by 80%. If his medi

In 2020, the medical expense of a person increased by 80%. If his medical expense in 2019 was 10% of his salary, then what percent of his salary was the medical expense in 2020?

20%

18%

16%

15%

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UPSC CBI DSP LDCE – 2023

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Let the person’s salary in 2019 be S.
His medical expense in 2019 was 10% of his salary, which is 0.10 * S.
In 2020, the medical expense increased by 80%. The increase amount is 80% of the 2019 expense.
Increase = 80% of (0.10 * S) = (80/100) * (0.10 * S) = 0.80 * 0.10 * S = 0.08 * S.
The medical expense in 2020 is the 2019 expense plus the increase:
Expense in 2020 = (0.10 * S) + (0.08 * S) = 0.18 * S.
To express this as a percentage of his salary in 2020 (assuming salary remained the same, as implied by the question structure), we have:
Percentage = (Expense in 2020 / Salary) * 100%
Percentage = (0.18 * S / S) * 100% = 0.18 * 100% = 18%.

The key is to calculate the increase amount based on the original expense and then add it to the original expense to find the new expense.

This is a straightforward percentage calculation problem. If the base for the percentage (salary) changes, the question would specify the change in salary as well. Since it doesn’t, we assume the salary remains constant relative to which the expense percentage is calculated.

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34. During the period 2016-2020, which company’s growth rate in profit is

During the period 2016-2020, which company’s growth rate in profit is the least?

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The correct answer is D) D.

Using the growth rates calculated for the period 2016-2020 from the previous question:
Growth Rate (2016-2020) = ((Profit in 2020 – Profit in 2016) / Profit in 2016) * 100%
Company A: ≈ 385.71%
Company B: ≈ 366.67%
Company C: 200%
Company D: 25%

Comparing these growth rates, the least growth rate during the period 2016-2020 is 25%, which belongs to Company D.

35. Which company’s growth rate in profit is the highest during the period

Which company’s growth rate in profit is the highest during the period 2016-2020?

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The correct answer is A) A.

The growth rate during the period 2016-2020 is calculated by comparing the profit in the final year (2020) to the profit in the initial year (2016).
Growth Rate (2016-2020) = ((Profit in 2020 – Profit in 2016) / Profit in 2016) * 100%
Company A: ((34 – 7) / 7) * 100% = (27 / 7) * 100% ≈ 385.71%
Company B: ((7 – 1.5) / 1.5) * 100% = (5.5 / 1.5) * 100% ≈ 366.67%
Company C: ((12 – 4) / 4) * 100% = (8 / 4) * 100% = 200%
Company D: ((25 – 20) / 20) * 100% = (5 / 20) * 100% = 25%

Comparing the calculated growth rates for the entire period: Company A (≈385.71%), Company B (≈366.67%), Company C (200%), Company D (25%). Company A has the highest growth rate during this period.

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36. The next three (3) items are based on the following data, where profit

The next three (3) items are based on the following data, where profits of four companies during the year 2016 to 2020 are displayed in rupees thousand crore :

Year	Company
Year	A	B	C	D
2016	7	1.5	4	20
2017	14	2	10	22
2018	25	6	14	23
2019	30	7	15	21
2020	34	7	12	25

Which company had maximum growth rate in profit with respect to the previous year in single year during the period 2016-2020?

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The correct answer is B) B.

To find the company with the maximum single-year growth rate, we calculate the percentage growth year-on-year for each company from 2017 to 2020 and find the maximum value among all these calculations.
Growth Rate = ((Profit in Current Year – Profit in Previous Year) / Profit in Previous Year) * 100%
Company A: Max growth = ((14 – 7) / 7) * 100% = 100% (2017 vs 2016)
Company B: Max growth = ((6 – 2) / 2) * 100% = 200% (2018 vs 2017)
Company C: Max growth = ((10 – 4) / 4) * 100% = 150% (2017 vs 2016)
Company D: Max growth = ((22 – 20) / 20) * 100% = 10% (2017 vs 2016)
Comparing the maximum single-year growth rates (100%, 200%, 150%, 10%), the highest is 200%, achieved by Company B.

Calculating other growth rates:
A: 2018 vs 2017: (25-14)/14 ≈ 78.6%; 2019 vs 2018: (30-25)/25 = 20%; 2020 vs 2019: (34-30)/30 ≈ 13.3%
B: 2019 vs 2018: (7-6)/6 ≈ 16.7%; 2020 vs 2019: (7-7)/7 = 0%
C: 2018 vs 2017: (14-10)/10 = 40%; 2019 vs 2018: (15-14)/14 ≈ 7.1%; 2020 vs 2019: (12-15)/15 = -20%
D: 2018 vs 2017: (23-22)/22 ≈ 4.5%; 2019 vs 2018: (21-23)/23 ≈ -8.7%; 2020 vs 2019: (25-21)/21 ≈ 19.0%
The maximum among all these single-year growth rates is indeed 200% for Company B.

37. If FATHER is coded as DCRJCT, then what is the code for UNCLE?

If FATHER is coded as DCRJCT, then what is the code for UNCLE?

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SPANC

SPANA

WLEJG

WLEGJ

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The correct answer is A) SPANC.

Analyzing the coding of FATHER (F-A-T-H-E-R) to DCRJCT (D-C-R-J-C-T), we observe a consistent pattern of letter shifts based on their alphabetical position:
F (6) -> D (4): Shift -2
A (1) -> C (3): Shift +2
T (20) -> R (18): Shift -2
H (8) -> J (10): Shift +2
E (5) -> C (3): Shift -2
R (18) -> T (20): Shift +2
The pattern of shifts is alternating -2, +2, -2, +2, -2, +2.

Applying this pattern to UNCLE:
U (21) -> U – 2 = S (19)
N (14) -> N + 2 = P (16)
C (3) -> C – 2 = A (1)
L (12) -> L + 2 = N (14)
E (5) -> E – 2 = C (3)
Thus, UNCLE is coded as SPANC.

38. Consider the following table : 3 8 5 2 11 9 1 -3 ?

Consider the following table :

3	8	5
2	11	9
1	-3	?

Which one of the following is the missing number in the above table?

-2

-4

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The correct answer is D) -4.

Observing the relationship between the numbers in each row, it appears that the third number in each row is the difference between the second number and the first number. Let’s verify:
Row 1: 8 – 3 = 5 (Correct)
Row 2: 11 – 2 = 9 (Correct)
Following this pattern for Row 3:
-3 – 1 = -4.

Another way to express the pattern is that the second number is the sum of the first and third numbers:
Row 1: 3 + 5 = 8 (Correct)
Row 2: 2 + 9 = 11 (Correct)
For Row 3: 1 + ? = -3. Solving for ? gives ? = -3 – 1 = -4. Both patterns lead to the same answer.

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39. What is the primary purpose of a firewall?

What is the primary purpose of a firewall?

Scans all your systems for existence of virus

Records your activities on the computer

Stops you from installing software that will harm your computer

Prevents unauthorized access to your computer via internet

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The correct answer is D) Prevents unauthorized access to your computer via internet.

The primary purpose of a firewall is to act as a security barrier that monitors and controls incoming and outgoing network traffic. It enforces security rules to block unauthorized connections and prevent malicious traffic from entering or leaving a network or individual computer, particularly via external networks like the internet.

Antivirus software scans for viruses. Recording activities is related to auditing or logging tools. Stopping software installation is usually managed by OS permissions or specific endpoint security software, not the primary function of a firewall.

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40. Which one of the following is a self-replicating program that eats up

Which one of the following is a self-replicating program that eats up the entire disk space as memory?

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Worm

Trojan Horse

Ransomware

Spyware

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The correct answer is A) Worm.

A worm is a standalone malware program that replicates itself to spread to other computers. Unlike viruses, worms do not need to attach themselves to an existing program. They can consume significant system resources, including disk space and memory, as they self-replicate and spread.

A Trojan Horse is a malicious program disguised as legitimate software, but it does not self-replicate. Ransomware encrypts data and demands payment for its release. Spyware collects information about the user’s activities without their knowledge. The description of a self-replicating program that consumes disk space aligns best with the characteristics of a worm.