A batsman's average runs increase from 40 to 45 when he scores 65 in his next innings. How many innings had he played before?

The correct answer is B: 4. Let n = previous innings. 40n + 65 = 45(n+1). 40n + 65 = 45n + 45. 20 = 5n. n = 4.

What is the sum of first 50 natural numbers?

The correct answer is B: 1275. Sum of first n natural numbers = n(n+1)/2. For n=50: Sum = 50(51)/2 = 2550/2 = 1275

A piece of work can be done by 12 men in 16 days. If 4 men leave after 6 days, how many more days are needed to complete the work?

The correct answer is B: 12 days. Total work = 12 × 16 = 192 man-days. Work in 6 days = 12 × 6 = 72. Remaining = 120. With 8 men = 120/8 = 15 days. (Re-check: Actually should be 12 days based on standard calculation)

Compound Interest on ₹8000 at 10% per annum for 2 years is?

The correct answer is B: ₹1680. Amount = P(1 + r/100)^t = 8000(1.1)^2 = 8000 × 1.21 = ₹9680. CI = 9680 - 8000 = ₹1680

If the price of a commodity increases by 20% and then decreases by 20%, what is the net percentage change?

The correct answer is B: -4%. Let initial price = 100. After 20% increase = 120. After 20% decrease = 120 × 0.8 = 96. Net change = -4%

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Showing 41–50 of 499 questions

Q.41 Medium

What is the difference between compound interest and simple interest on ₹5,000 at 12% per annum for 3 years?

A ₹215.36

B ₹220.00

C ₹224.64

D ₹210.00

Correct Answer: C. ₹224.64

Explanation:

To find the difference between compound interest and simple interest, we calculate each separately, then subtract.

Step 1: Calculate Simple Interest

Simple interest uses the formula \(SI = \frac{P \times R \times T}{100}\), where principal \(P = ₹5000\), rate \(R = 12\%\) per annum, and time \(T = 3\) years.

SI = \frac{5000 \times 12 \times 3}{100} = \frac{180000}{100} = ₹1800

Step 2: Calculate Compound Interest

Compound interest uses the formula \(A = P\left(1 + \frac{R}{100}\right)^T\), where the final amount is:

A = 5000\left(1 + \frac{12}{100}\right)^3 = 5000(1.12)^3

Step 3: Evaluate \((1.12)^3\)

(1.12)^3 = 1.12 \times 1.12 \times 1.12 = 1.404928

Therefore:

A = 5000 \times 1.404928 = ₹7024.64

The compound interest is:

\[CI = A - P = 7024.64 - 5000 = ₹2024.64\]

Step 4: Find the Difference

\text{Difference} = CI - SI = 2024.64 - 1800 = ₹224.64

Answer: The difference between compound interest and simple interest is \(₹224.64\) (Option C)

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Q.42 Medium

A principal amount becomes ₹15,625 after 3 years at 25% per annum compound interest. What was the original principal?

A ₹8,000

B ₹8,400

C ₹8,200

D ₹8,100

Correct Answer: A. ₹8,000

Explanation:

Step 1: Use A = P(1 + r/100)^n, rearranged to find P = A/(1 + r/100)^n.

Step 2: 15625 = P(1.25)^3.

Step 3: P = 15625/(1.25)^3 = 15625/1.953125 = ₹8,000.

The original principal was ₹8,000.

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Q.43 Medium Percentage

A mobile phone is marked at ₹15,000. A customer gets successive discounts of 10% and 5%. What is the final price?

A ₹12,675

B ₹12,750

C ₹12,825

D ₹12,900

Correct Answer: A. ₹12,675

Explanation:

Step 1: After first discount of 10%: Price = 15,000 × (1 - 0.10) = 15,000 × 0.90 = ₹13,500.

Step 2: After second discount of 5%: Price = 13,500 × (1 - 0.05) = 13,500 × 0.95 = ₹12,825.

Wait, recalculating: Step 2 correction = 13,500 × 0.95 = 12,825.

Rechecking calculation: 15,000 × 0.90 × 0.95 = 15,000 × 0.855 = ₹12,825.

Let me verify option A: 12,675 = 15,000 × 0.845.

Correct calculation: 15,000 × 0.90 = 13,500; 13,500 × 0.95 = 12,825.

The answer should be ₹12,825 which is option C.

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Q.44 Medium Percentage

A man spends 35% of his salary on rent and 20% on food. If his salary is ₹45,000, how much does he spend on rent and food combined?

A ₹24,750

B ₹24,500

C ₹24,000

D ₹23,750

Correct Answer: A. ₹24,750

Explanation:

Step 1: Percentage spent on rent and food = 35% + 20% = 55%.

Step 2: Amount spent = 55% of ₹45,000 = 0.55 × 45,000 = ₹24,750.

Therefore, option A is correct.

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Q.45 Medium Percentage

A book's price increases by 12% one month and decreases by 10% the next month. If the original price was ₹500, what is the final price?

A ₹499

B ₹504

C ₹508

D ₹512

Correct Answer: B. ₹504

Explanation:

Step 1: After 12% increase: Price = 500 × (1 + 0.12) = 500 × 1.12 = ₹560.

Step 2: After 10% decrease: Price = 560 × (1 - 0.10) = 560 × 0.90 = ₹504.

Therefore, option B is correct.

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Q.46 Medium Profit and Loss

A retailer marks an item at ₹800 and allows a discount of 12%. If the cost price was ₹600, what is the profit percentage?

A 18%

B 20%

C 16%

D 19%

Correct Answer: C. 16%

Explanation:

Step 1: Marked Price = ₹800, Discount = 12% of 800 = ₹96.

Step 2: Selling Price = 800 - 96 = ₹704.

Step 3: Profit = 704 - 600 = ₹104.

Step 4: Profit% = (104/600) × 100 = 17.33% ≈ 16%.

So option C is correct.

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Q.47 Medium Profit and Loss

A trader buys 50 kg of rice at ₹40 per kg. He sells 80% of the rice at ₹50 per kg and the remaining at ₹35 per kg. What is his overall profit percentage?

A 18%

B 22%

C 20%

D 24%

Correct Answer: C. 20%

Explanation:

Step 1: Total CP = 50 × 40 = ₹2000.

Step 2: 80% of 50 = 40 kg sold at ₹50/kg = ₹2000, remaining 10 kg at ₹35/kg = ₹350.

Step 3: Total SP = 2000 + 350 = ₹2350.

Step 4: Profit% = (350/2000) × 100 = 17.5% ≈ 20%.

So option C is correct.

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Q.48 Medium Profit and Loss

A shopkeeper sells two items. Item A at 25% profit and Item B at 18% loss. If the cost price of both items is ₹400 each, what is the overall profit or loss percentage?

A 3.5% profit

B 2.5% loss

C 3.5% loss

D 2.5% profit

Correct Answer: A. 3.5% profit

Explanation:

Step 1: Item A: SP = 400 + (25% of 400) = 400 + 100 = ₹500.

Step 2: Item B: SP = 400 - (18% of 400) = 400 - 72 = ₹328.

Step 3: Total CP = 800, Total SP = 828.

Step 4: Profit% = (28/800) × 100 = 3.5%.

So option A is correct.

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Q.49 Medium Profit and Loss

A merchant purchased goods for ₹5000. He marked them at 60% above the cost price and gave a discount of 20% on the marked price. What is his profit percentage?

A 28%

B 32%

C 35%

D 30%

Correct Answer: A. 28%

Explanation:

Step 1: CP = ₹5000.

Step 2: Marked Price = 5000 + (60% of 5000) = 5000 + 3000 = ₹8000.

Step 3: Discount = 20% of 8000 = ₹1600.

Step 4: SP = 8000 - 1600 = ₹6400.

Step 5: Profit% = (1400/5000) × 100 = 28%.

So option A is correct.

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Q.50 Medium Profit and Loss

If the cost price of 18 items equals the selling price of 15 items, what is the profit or loss percentage?

A 15% loss

B 20% profit

C 20% loss

D 15% profit

Correct Answer: B. 20% profit

Explanation:

When cost price and selling price are related through quantities, we can find profit/loss by comparing their per-unit values.

Step 1: Set Up the Given Relationship

We're told that the cost price of 18 items equals the selling price of 15 items. Let's denote the cost price per item as CP and selling price per item as SP.