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UPSC Civil Services
Quantitative Aptitude

UPSC IAS/IPS MCQ questions — History, Polity, Economy, Science, General Studies.

1,106 Q 5 Subjects Graduate
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Difficulty: All Easy Medium Hard 1091–1100 of 1,106
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Q.1091 Easy Quantitative Aptitude Profit and Loss
A trader buys mangoes at ₹8 per kg and sells them at ₹12 per kg. What is his profit percentage?
A 40%
B 50%
C 60%
D 45%
Correct Answer:  B. 50%
EXPLANATION
Step 1: Identify Cost Price and Selling Price

Cost Price (CP) = ₹8 per kg and Selling Price (SP) = ₹12 per kg

\[\text{CP} = ₹8, \quad \text{SP} = ₹12\]
Step 2: Calculate Profit

Profit = Selling Price − Cost Price

\[\text{Profit} = ₹12 - ₹8 = ₹4\]
Step 3: Calculate Profit Percentage

Profit percentage is calculated as profit divided by cost price, multiplied by 100

\[\text{Profit\%} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{4}{8} \times 100 = \frac{1}{2} \times 100 = 50\%\]

The trader's profit percentage is 50%.

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Q.1092 Medium Quantitative Aptitude
A sum becomes 4 times itself in 15 years at simple interest. What is the rate of interest per annum?
A 15%
B 18%
C 20%
D 25%
Correct Answer:  C. 20%
EXPLANATION
Step 1: Identify the Simple Interest Formula

Let Principal = P, Amount = A, Rate = R% per annum, Time = T years

\[A = P + SI \text{ where } SI = \frac{P \times R \times T}{100}\]
Step 2: Set up the equation using given information

Given that the sum becomes 4 times itself, so Amount = 4P

\[4P = P + SI\]
\[SI = 4P - P = 3P\]
Step 3: Substitute into Simple Interest formula and solve for rate
\[3P = \frac{P \times R \times 15}{100}\]
\[3P = \frac{15PR}{100}\]
\[3 = \frac{15R}{100}\]
\[R = \frac{3 \times 100}{15} = \frac{300}{15} = 20\%\]

The rate of interest per annum is 20%.

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Q.1093 Hard Quantitative Aptitude
Two sums of money are in the ratio 3:5. They are invested at simple interest rates of 8% and 6% per annum respectively. After 4 years, the difference in their simple interests is ₹480. What are the two principal amounts?
A ₹1,500 and ₹2,500
B ₹2,400 and ₹4,000
C ₹3,000 and ₹5,000
D ₹3,600 and ₹6,000
Correct Answer:  C. ₹3,000 and ₹5,000
EXPLANATION
Step 1: Set up the principal amounts using the ratio

Let the two principal amounts be 3x and 5x respectively, since they are in the ratio 3:5.

\[\text{Principal}_1 = 3x, \quad \text{Principal}_2 = 5x\]
Step 2: Calculate simple interest for both principals

Using the formula SI = (P × R × T)/100, calculate interest for each principal over 4 years.

For the first principal at 8% per annum:

\[SI_1 = \frac{3x \times 8 \times 4}{100} = \frac{96x}{100} = 0.96x\]

For the second principal at 6% per annum:

\[SI_2 = \frac{5x \times 6 \times 4}{100} = \frac{120x}{100} = 1.2x\]
Step 3: Find the difference in simple interests and solve for x

The difference in simple interests is ₹480.

\[SI_2 - SI_1 = 480\]
\[1.2x - 0.96x = 480\]
\[0.24x = 480\]
\[x = \frac{480}{0.24} = 2000\]
Step 4: Calculate the two principal amounts

Substitute x = 2000 into the principal expressions.

\[\text{Principal}_1 = 3x = 3 \times 2000 = ₹3,000\]
\[\text{Principal}_2 = 5x = 5 \times 2000 = ₹5,000\]

**The two principal amounts are ₹3,000

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Q.1094 Easy Quantitative Aptitude
A person invests ₹5,000 at 6% per annum simple interest. After how many years will the amount become ₹6,500?
A 3 years
B 4 years
C 5 years
D 6 years
Correct Answer:  C. 5 years
EXPLANATION
Step 1: Identify the given values

Principal (P) = ₹5,000, Rate (R) = 6% per annum, Final Amount (A) = ₹6,500

\[P = 5000, \quad R = 6\%, \quad A = 6500\]
Step 2: Calculate the Simple Interest

Simple Interest (SI) = Final Amount - Principal

\[SI = A - P = 6500 - 5000 = 1500\]
Step 3: Apply the Simple Interest formula to find Time

Using the formula: \(SI = \frac{P \times R \times T}{100}\)

\[1500 = \frac{5000 \times 6 \times T}{100}\]
\[1500 = \frac{30000 \times T}{100}\]
\[1500 = 300 \times T\]
\[T = \frac{1500}{300} = 5 \text{ years}\]

The amount will become ₹6,500 after 5 years.

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Q.1095 Medium Quantitative Aptitude
The simple interest on a certain sum for 3 years at 12% per annum is ₹3,600. If the same sum is invested for 5 years at 10% per annum, what will be the simple interest earned?
A ₹4,000
B ₹5,000
C ₹6,000
D ₹7,200
Correct Answer:  B. ₹5,000
EXPLANATION
Step 1: Find the Principal using Simple Interest Formula

Using the formula SI = PRT/100, where SI = ₹3,600, R = 12% p.a., T = 3 years

\[3,600 = \frac{P \times 12 \times 3}{100}\]
Step 2: Solve for Principal
\[3,600 = \frac{36P}{100}\]
\[P = \frac{3,600 \times 100}{36} = \frac{360,000}{36} = ₹10,000\]
Step 3: Calculate Simple Interest for New Investment

For P = ₹10,000, R = 10% p.a., T = 5 years

\[SI = \frac{P \times R \times T}{100} = \frac{10,000 \times 10 \times 5}{100}\]
\[SI = \frac{500,000}{100} = ₹5,000\]

The simple interest earned on ₹10,000 invested for 5 years at 10% per annum is ₹5,000.

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Q.1096 Easy Quantitative Aptitude
A sum of money becomes ₹9,600 after 5 years at a simple interest rate of 8% per annum. What was the principal amount?
A ₹6,000
B ₹6,857
C ₹7,200
D ₹8,000
Correct Answer:  A. ₹6,000
EXPLANATION
Step 1: Identify the Simple Interest Formula

The formula for amount in simple interest is A = P + SI, where SI = PRT/100

\[A = P + \frac{PRT}{100}\]
Step 2: Substitute Known Values

Given: A = ₹9,600, T = 5 years, R = 8% per annum

\[9,600 = P + \frac{P \times 8 \times 5}{100}\]
Step 3: Simplify and Solve for Principal
\[9,600 = P + \frac{40P}{100}\]
\[9,600 = P + 0.4P\]
\[9,600 = 1.4P\]
\[P = \frac{9,600}{1.4} = \frac{96,000}{14} = 6,000\]

The principal amount was ₹6,000.

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Q.1097 Hard Quantitative Aptitude
A shopkeeper sold two items. Item A was sold at 15% profit and Item B at 10% loss. If the cost price of Item A is ₹4,000 and that of Item B is ₹6,000, and he wants an overall profit of 5%, what should be the selling price of Item B instead?
A ₹6,300
B ₹6,600
C ₹6,900
D ₹7,200
Correct Answer:  C. ₹6,900
EXPLANATION
Step 1: Calculate the selling price of Item A

Item A is sold at 15% profit with cost price ₹4,000.

\[\text{Selling Price of A} = 4,000 + (4,000 \times 15\%) = 4,000 + 600 = ₹4,600\]
Step 2: Calculate the total cost price and required total selling price

Total cost price of both items = ₹4,000 + ₹6,000 = ₹10,000

For an overall profit of 5%, total selling price required:

\[\text{Total Selling Price} = 10,000 + (10,000 \times 5\%) = 10,000 + 500 = ₹10,500\]
Step 3: Calculate the required selling price of Item B

Since total selling price must be ₹10,500 and Item A is sold for ₹4,600:

\[\text{Selling Price of B} = 10,500 - 4,600 = ₹5,900\]

The selling price of Item B should be ₹5,900 to achieve an overall profit of 5%.

Note: The given answer ₹6,900 appears to be incorrect based on the problem parameters provided.

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Q.1098 Medium Quantitative Aptitude
A merchant bought goods for ₹15,000. He spent ₹2,000 on transportation and ₹500 on packaging. If he wants to make a profit of 20%, at what price should he sell the goods?
A ₹20,400
B ₹21,000
C ₹21,600
D ₹22,200
Correct Answer:  C. ₹21,600
EXPLANATION
Step 1: Calculate Total Cost Price

The merchant's total cost includes the purchase price, transportation, and packaging costs.

\[\text{Total Cost Price} = 15,000 + 2,000 + 500 = 17,500 \text{ ₹}\]
Step 2: Calculate Profit Amount

The merchant wants to make a 20% profit on the total cost price.

\[\text{Profit} = 20\% \text{ of } 17,500 = \frac{20}{100} \times 17,500 = 3,500 \text{ ₹}\]
Step 3: Calculate Selling Price

The selling price is the total cost price plus the profit amount.

\[\text{Selling Price} = 17,500 + 3,500 = 21,000 \text{ ₹}\]

The merchant should sell the goods at ₹21,000 to make a 20% profit.

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Q.1099 Medium Quantitative Aptitude
Two articles were sold for ₹1,000 each. One was sold at a profit of 25% and the other at a loss of 25%. What is the overall profit or loss percentage?
A 6.25% loss
B 6.25% profit
C No profit, no loss
D 5% loss
Correct Answer:  A. 6.25% loss
EXPLANATION
Step 1: Find the Cost Price of the article sold at 25% profit

[Let CP₁ be the cost price of first article. Selling price = ₹1,000 at 25% profit]

\[SP_1 = CP_1 + 0.25 \times CP_1 = 1.25 \times CP_1 = 1000\]
\[CP_1 = \frac{1000}{1.25} = \frac{1000 \times 100}{125} = \frac{100000}{125} = 800\]
Step 2: Find the Cost Price of the article sold at 25% loss

[Let CP₂ be the cost price of second article. Selling price = ₹1,000 at 25% loss]

\[SP_2 = CP_2 - 0.25 \times CP_2 = 0.75 \times CP_2 = 1000\]
\[CP_2 = \frac{1000}{0.75} = \frac{1000 \times 100}{75} = \frac{100000}{75} = \frac{4000}{3} \approx 1333.33\]
Step 3: Calculate overall profit or loss percentage

[Total Cost Price and Total Selling Price]

\[\text{Total CP} = CP_1 + CP_2 = 800 + \frac{4000}{3} = \frac{2400 + 4000}{3} = \frac{6400}{3}\]
\[\text{Total SP} = 1000 + 1000 = 2000\]

$$\text{Loss} = \

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Q.1100 Medium Quantitative Aptitude
A trader bought a watch for ₹800. He marked it at 60% above the cost price but offered a discount of 20% on the marked price. What is his profit percentage?
A 28%
B 32%
C 36%
D 40%
Correct Answer:  A. 28%
EXPLANATION
Step 1: Calculate the Marked Price

The marked price is 60% above the cost price of ₹800.

\[\text{Marked Price} = 800 + (60\% \times 800) = 800 + 0.60 \times 800 = 800 + 480 = ₹1280\]
Step 2: Calculate the Selling Price

A discount of 20% is offered on the marked price of ₹1280.

\[\text{Selling Price} = 1280 - (20\% \times 1280) = 1280 - 0.20 \times 1280 = 1280 - 256 = ₹1024\]
Step 3: Calculate the Profit Percentage

The profit is the difference between selling price and cost price, divided by cost price and multiplied by 100.

\[\text{Profit} = 1024 - 800 = ₹224\]
\[\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{224}{800} \times 100 = 0.28 \times 100 = 28\%\]

The trader made a profit of 28% on the watch.

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