A trader buys cotton fabric at ₹450 per meter. He marks it at 60% above cost price but allows a 10% discount. What is his profit percentage?

The correct answer is B: 44%. Step 1: CP = ₹450. Marked Price = 450 × 1.60 = ₹720. Step 2: SP after 10% discount = 720 × 0.90 = ₹648. Step 3: Profit% = [(648 - 450)/450] × 100 = (198/450) × 100 = 44%. So option B is correct.

Principal ₹5000, Rate 8% per annum, Time 2 years. Find Simple Interest.

The correct answer is C: ₹800. SI = (P × R × T)/100 = (5000 × 8 × 2)/100 = ₹800

The ratio of speeds of two trains is 3:4. They travel towards each other. If they meet after 4 hours and the slower train covers 240 km, what is the distance between the two stations?

The correct answer is A: 560 km. When two objects travel towards each other, their combined distance equals the sum of distances covered by each object individually. Step 1: **Find the Speed of the Slower Train** The slower train covers 240 km in 4 hours, so we can calculate its speed directly. $$\text{Speed of slower train} = \fra

What is the GCD of 144, 180, and 216?

The correct answer is D: 36. 144 = 2⁴ × 3², 180 = 2² × 3² × 5, 216 = 2³ × 3³. GCD = 2² × 3² = 4 × 9 = 36.

A commodity's price increases by 25% in the first year and decreases by 20% in the second year. If the initial price was Rs. 1000, what is the price after 2 years?

The correct answer is C: Rs. 1000. To find the final price after two successive percentage changes, apply each change sequentially to the original price. **Step 1: Calculate price after 25% increase in Year 1** Initial price = Rs. 1000 A 25% increase means the new price is 125% of the original: \[ \text{Price after Year 1} = 1000 \ti

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Q.191 Medium Numbers

A boat takes 4 hours to travel 60 km downstream and 6 hours to travel 60 km upstream. What is the stream's speed?

A2.5 km/h

B5 km/h

C7.5 km/h

D10 km/h

Correct Answer: A. 2.5 km/h

Explanation:

Downstream speed = 15 km/h. Upstream speed = 10 km/h. Stream speed = (15-10)/2 = 2.5 km/h.

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Q.192 Medium Numbers

If 15 workers can complete a project in 20 days, how many workers are needed to complete it in 12 days?

A20 workers

B25 workers

C30 workers

D35 workers

Correct Answer: B. 25 workers

Explanation:

Total work = 15 × 20 = 300 worker-days. Workers needed = 300/12 = 25.

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Q.193 Medium Numbers

A merchant marks goods 50% above cost price and offers a discount. If he makes 25% profit, what is the discount percentage?

A16.67%

B20%

C25%

D33.33%

Correct Answer: A. 16.67%

Explanation:

Let CP = 100. MP = 150. For 25% profit, SP = 125. Discount = (150-125)/150 × 100 = 16.67%.

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Q.194 Medium Numbers

What is the difference between compound interest and simple interest on Rs. 20000 at 10% per annum for 2 years?

ARs. 100

BRs. 200

CRs. 300

DRs. 400

Correct Answer: B. Rs. 200

Explanation:

SI = (20000 × 10 × 2)/100 = 4000. CI = 20000(1.1)² - 20000 = 24200 - 20000 = 4200. Difference = 200.

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Q.195 Medium Numbers

Two trains start from stations 360 km apart and move towards each other at speeds of 50 km/h and 70 km/h respectively. In how many hours will they meet?

A2 hours

B2.5 hours

C3 hours

D3.5 hours

Correct Answer: C. 3 hours

Explanation:

Combined speed = 50 + 70 = 120 km/h. Time = 360/120 = 3 hours.

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Q.196 Medium Numbers

A man's salary is increased by 20%, then decreased by 10%. What is the net percentage change?

A8%

B10%

C12%

D15%

Correct Answer: A. 8%

Explanation:

Let salary = 100. After increase: 120. After decrease: 120 × 0.9 = 108. Net change = 8%.

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Q.197 Medium Numbers

If a person walks at 5 km/h, he reaches his office 10 minutes late. If he walks at 6 km/h, he reaches 5 minutes early. What is the distance to the office?

A5 km

B7.5 km

C10 km

D12.5 km

Correct Answer: B. 7.5 km

Explanation:

This problem involves using the relationship between distance, speed, and time where the same distance is covered in different times at different speeds.

Step 1: Set Up Equations Using Distance Formula

Let the distance be d km and the required time be t hours. Since distance = speed × time, we can write two equations based on the given conditions.

d = 5\left(t + \frac{10}{60}\right) = 5\left(t + \frac{1}{6}\right)

d = 6\left(t - \frac{5}{60}\right) = 6\left(t - \frac{1}{12}\right)

Step 2: Solve for Time

Since both expressions equal d, we set them equal and solve for t.

5\left(t + \frac{1}{6}\right) = 6\left(t - \frac{1}{12}\right)

5t + \frac{5}{6} = 6t - \frac{6}{12}

5t + \frac{5}{6} = 6t - \frac{1}{2}

\frac{5}{6} + \frac{1}{2} = 6t - 5t

\frac{5}{6} + \frac{3}{6} = t

t = \frac{8}{6} = \frac{4}{3} \text{ hours}

Step 3: Calculate Distance

Substitute t back into either equation to find d.

d = 5\left(\frac{4}{3} + \frac{1}{6}\right) = 5\left(\frac{8}{6} + \frac{1}{6}\right) = 5 \times \frac{9}{6} = 5 \times \frac{3}{2} = \frac{15}{2} = 7.5 \text{ km}

The distance to the office is 7.5 km.

Let the distance to the office be d km.

Time taken at 5 km/h:

5

d

hours

Time taken at 6 km/h:

6

d

hours

The difference in arrival times is:

10 minutes late at 5 km/h

5 minutes early at 6 km/h

So, total difference =15 minutes =

60

15

=

4

1

hour.

Thus,

5

d

−

6

d

=

4

1

d(

5

1

−

6

1

)=

4

1

d(

30

6−5

)=

4

1

30

d

=

4

1

d=30×

4

1

=7.5

Therefore, the distance to the office is:

7.5 km

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Q.198 Medium Numbers

A trader marks an item 50% above cost price and gives 20% discount. What is the profit percentage?

A25%

B30%

C35%

D20%

Correct Answer: D. 20%

Explanation:

Let CP = 100. MP = 150. SP = 150 × 0.8 = 120. Profit = 20%

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Q.199 Medium Numbers

A man can complete a work in 12 days. A woman can complete it in 15 days. If they work together, in how many days will they complete it?

A6.5 days

B6.67 days

C7 days

D7.5 days

Correct Answer: B. 6.67 days

Explanation:

Work rate combined = 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Time = 20/3 ≈ 6.67 days

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Q.200 Medium Numbers

A stream flows at 2 km/h. A boat travels 30 km upstream in 5 hours. What is the boat's speed in still water?

A5 km/h

B6 km/h

C7 km/h

D8 km/h

Correct Answer: D. 8 km/h

Explanation:

Upstream speed = 30/5 = 6 km/h. Boat speed = Upstream speed + Stream speed = 6 + 2 = 8 km/h

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