State PSC Exam Preparation — BPSC, UPPSC, MPPSC

Q.1 Easy

A train travels 240 km in 4 hours. If it increases its speed by 20%, how much distance will it cover in 5 hours at the new speed?

A300 km

B360 km

C330 km

D288 km

Correct Answer: B. 360 km

Explanation:

Step 1: Calculate the original speed

The train travels 240 km in 4 hours, so we divide distance by time.

\text{Original Speed} = \frac{240 \text{ km}}{4 \text{ hours}} = 60 \text{ km/h}

Step 2: Calculate the new speed after 20% increase

The speed increases by 20%, so we multiply the original speed by 1.20.

\text{New Speed} = 60 \times 1.20 = 72 \text{ km/h}

Step 3: Calculate distance covered in 5 hours at new speed

Distance equals speed multiplied by time.

\text{Distance} = 72 \text{ km/h} \times 5 \text{ hours} = 360 \text{ km}

The train will cover 360 km in 5 hours at the new speed.

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Q.2 Medium

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?

A10 km

B12 km

C11 km

D15 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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Q.3 Hard

Two cyclists start simultaneously from the same point and travel in opposite directions on a circular track of 600 m. If their speeds are 8 m/s and 10 m/s respectively, after how much time will they meet again at the starting point?

A100 seconds

B150 seconds

C200 seconds

D300 seconds

Correct Answer: C. 200 seconds

Explanation:

Step 1: Find the time for each cyclist to complete one full lap

[Cyclist 1 completes one lap]

\text{Time}_1 = \frac{\text{Track length}}{\text{Speed}_1} = \frac{600}{8} = 75 \text{ seconds}

[Cyclist 2 completes one lap]

\text{Time}_2 = \frac{\text{Track length}}{\text{Speed}_2} = \frac{600}{10} = 60 \text{ seconds}

Step 2: Find the LCM of their lap times

[The cyclists will meet at the starting point when the time elapsed is a common multiple of both lap times]

\text{LCM}(75, 60) = \text{LCM of lap times}

[Finding prime factorization: 75 = 3 × 5², 60 = 2² × 3 × 5]

\text{LCM}(75, 60) = 2^2 \times 3 \times 5^2 = 4 \times 3 \times 25 = 300 \text{ seconds}

Step 3: Verify the answer

[In 300 seconds, Cyclist 1 completes]

\text{Laps}_1 = \frac{300}{75} = 4 \text{ laps}

[In 300 seconds, Cyclist 2 completes]

\text{Laps}_2 = \frac{300}{60} = 5 \text{ laps}

[Both return to the starting point after completing whole laps

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Q.4 Medium

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?

A17.5 km/h

B15 km/h

C16 km/h

D18 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.5 Hard

A car travels at 60 km/h for the first half of the distance and at 90 km/h for the second half of the distance. What is the average speed for the entire journey?

A72 km/h

B75 km/h

C70 km/h

D74 km/h

Correct Answer: A. 72 km/h

Explanation:

Step 1: Define Variables and Total Distance

Let the total distance be $D$ km. The car travels $\frac{D}{2}$ km at each speed.

\text{Total Distance} = D \text{ km}

Step 2: Calculate Time for Each Half

For the first half at 60 km/h:

t_1 = \frac{D/2}{60} = \frac{D}{120} \text{ hours}

For the second half at 90 km/h:

t_2 = \frac{D/2}{90} = \frac{D}{180} \text{ hours}

Step 3: Calculate Total Time and Average Speed

Total time for the journey:

t_{\text{total}} = \frac{D}{120} + \frac{D}{180} = \frac{3D}{360} + \frac{2D}{360} = \frac{5D}{360} = \frac{D}{72} \text{ hours}

Average speed is total distance divided by total time:

\text{Average Speed} = \frac{D}{t_{\text{total}}} = \frac{D}{\frac{D}{72}} = 72 \text{ km/h}

The average speed for the entire journey is 72 km/h.

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Q.6 Easy

A shopkeeper buys notebooks at ₹40 each and sells them at ₹50 each. If he sells 120 notebooks in a day, what is his total profit?

A₹1,200

B₹1,500

C₹1,800

D₹2,000

Correct Answer: A. ₹1,200

Explanation:

Step 1: Calculate Total Cost Price

The shopkeeper buys 120 notebooks at ₹40 each.

\text{Total Cost Price} = 120 \times 40 = ₹4,800

Step 2: Calculate Total Selling Price

The shopkeeper sells 120 notebooks at ₹50 each.

\text{Total Selling Price} = 120 \times 50 = ₹6,000

Step 3: Calculate Total Profit

Profit is the difference between selling price and cost price.

\text{Total Profit} = \text{Selling Price} - \text{Cost Price} = 6,000 - 4,800 = ₹1,200

The shopkeeper's total profit for selling 120 notebooks in a day is ₹1,200.

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Q.7 Medium

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?

A28%

B32%

C36%

D40%

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.8 Medium

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?

A6.25% loss

B6.25% profit

CNo profit, no loss

D5% 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.9 Medium

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.10 Hard

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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