Quantitative Aptitude Questions & Answers

Q.491 Medium Profit and Loss

An item was sold for ₹1,200 at a loss of 20%. At what price should it be sold to make a profit of 20%?

A ₹1,750

B ₹1,800

C ₹1,850

D ₹1,900

Correct Answer: B. ₹1,800

EXPLANATION

Step 1: SP at 20% loss = ₹1200, so CP = 1200/0.80 = ₹1500.

Step 2: For 20% profit: New SP = CP × (1 + 20/100) = 1500 × 1.20 = ₹1800.

So option B is correct.

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Q.492 Medium Profit and Loss

A shopkeeper marks an article at ₹500 and gives a discount of 20%. If he still makes a profit of 25%, what was the cost price?

A ₹315

B ₹320

C ₹325

D ₹330

Correct Answer: B. ₹320

EXPLANATION

Step 1: Calculate the Selling Price after discount

The marked price is ₹500 and discount is 20%.

\text{Selling Price} = 500 - (20\% \text{ of } 500) = 500 - \frac{20}{100} \times 500

\[= 500 - 100 = ₹400\]

Step 2: Use the profit formula to find Cost Price

The shopkeeper makes a profit of 25%, which means Selling Price is 125% of Cost Price.

\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit\%}}{100}\right)

400 = \text{Cost Price} \times \left(1 + \frac{25}{100}\right)

400 = \text{Cost Price} \times 1.25

Step 3: Solve for Cost Price

\text{Cost Price} = \frac{400}{1.25} = \frac{400}{\frac{5}{4}} = 400 \times \frac{4}{5}

= \frac{1600}{5} = ₹320

The cost price of the article is ₹320.

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Q.493 Medium Simple Interest

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.494 Medium Simple Interest

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.495 Medium Profit and Loss

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.496 Medium Profit and Loss

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.497 Medium Profit and Loss

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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Q.498 Medium Speed Distance Time

A boat takes 6 hours to travel 120 km downstream and 8 hours to travel the same distance upstream. What is the speed of the boat in still water?

A 17.5 km/h

B 15 km/h

C 16 km/h

D 18 km/h

Correct Answer: A. 17.5 km/h

EXPLANATION

Step 1: Find the downstream speed

The boat travels 120 km downstream in 6 hours.

\text{Downstream speed} = \frac{120}{6} = 20 \text{ km/h}

Step 2: Find the upstream speed

The boat travels 120 km upstream in 8 hours.

\text{Upstream speed} = \frac{120}{8} = 15 \text{ km/h}

Step 3: Calculate the speed of boat in still water

The speed of boat in still water is the average of downstream and upstream speeds.

\text{Speed of boat} = \frac{\text{Downstream speed} + \text{Upstream speed}}{2} = \frac{20 + 15}{2} = \frac{35}{2} = 17.5 \text{ km/h}

The speed of the boat in still water is 17.5 km/h.

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Q.499 Medium Speed Distance Time

A man walks from point A to point B at 4 km/h and returns from B to A at 6 km/h. If the total journey takes 5 hours, what is the distance between A and B?

A 10 km

B 12 km

C 11 km

D 15 km

Correct Answer: B. 12 km

EXPLANATION

Step 1: Define Variables and Set Up Equations

Let the distance between A and B be $d$ km. Time to go from A to B at 4 km/h is $\frac{d}{4}$ hours, and time to return from B to A at 6 km/h is $\frac{d}{6}$ hours.

\text{Total time} = \frac{d}{4} + \frac{d}{6} = 5

Step 2: Find Common Denominator and Simplify

The common denominator of 4 and 6 is 12. Rewrite each fraction with denominator 12.

\frac{3d}{12} + \frac{2d}{12} = 5

Step 3: Solve for Distance

Combine the fractions on the left side and solve for $d$.

\frac{5d}{12} = 5

5d = 5 \times 12

\[5d = 60\]

d = 12 \text{ km}

The distance between A and B is 12 km.

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