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

The correct answer is C: ₹224.64. 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

Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

The correct answer is B: 12 hours. Combined rate = 1/20 + 1/30 = 5/60 = 1/12. Time = 12 hours.

Which number is NOT divisible by 6?

The correct answer is D: 104. For divisibility by 6, number must be divisible by both 2 and 3. 104÷6 = 17.33... (not divisible). Others: 72, 84, 90 are all divisible by 6

A compound interest is earned on ₹10,000 at 8% per annum for 2 years. What is the average annual interest?

The correct answer is B: ₹816. CI for 2 years = 10000(1.08)² - 10000 = 10000(1.1664) - 10000 = 1664. Average annual interest = 1664/2 = 832. Wait, that's option C. Let me verify: A = 10000 × 1.08² = 11664. CI = 1664. Average per year = 1664/2 = 832. But option C is 832. Recalculating interest earned = 11664 - 10000 = 1664. Averag

Find the LCM of 20 and 30.

The correct answer is B: 60. 20 = 2² × 5, 30 = 2 × 3 × 5. LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60.

Corporate & IT Interview Preparation

Q.281 Easy HCF and LCM

A man's salary increases from ₹40,000 to ₹48,000. What is the percentage increase?

A 15%

B 18%

C 20%

D 22%

Correct Answer: C. 20%

Explanation:

Increase = 48000 - 40000 = 8000. Percentage = 8000/40000 × 100 = 20%.

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Q.282 Easy HCF and LCM

A man walks 5 km/h and covers a distance in 6 hours. If he walks at 6 km/h, how much time saved?

A 0.5 hour

B 1 hour

C 1.5 hours

D 2 hours

Correct Answer: B. 1 hour

Explanation:

Distance = 5×6 = 30 km. New time = 30/6 = 5 hours. Time saved = 6-5 = 1 hour.

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Q.283 Easy HCF and LCM

HCF of two numbers is 16. Their LCM is 960. Find the product of the numbers.

A 15,360

B 16,384

C 18,432

D 20,480

Correct Answer: A. 15,360

Explanation:

HCF×LCM = product of numbers. 16×960 = 15,360.

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Q.284 Easy HCF and LCM

The HCF of two numbers is 18 and their LCM is 1080. If one number is 108, find the other number.

A 180

B 162

C 216

D 144

Correct Answer: A. 180

Explanation:

Using HCF × LCM = Product of two numbers: 18 × 1080 = 108 × x; x = 19440/108 = 180

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Q.285 Easy HCF and LCM

Three bells ring at intervals of 6, 9, and 15 minutes respectively. They ring together at 9:00 AM. At what time will they ring together again?

A 9:45 AM

B 10:00 AM

C 9:30 AM

D 10:30 AM

Correct Answer: D. 10:30 AM

Explanation:

To find when the three bells ring together again, we need to find the Least Common Multiple (LCM) of their ringing intervals.

Step 1: Find the prime factorization of each interval

6 = 2 \times 3

\[9 = 3^2\]

15 = 3 \times 5

Step 2: Determine the LCM

The LCM is found by taking the highest power of each prime factor:

\text{LCM}(6, 9, 15) = 2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90

Step 3: Add 90 minutes to the initial time

The bells ring together at 9:00 AM. They will ring together again after 90 minutes.

90 \text{ minutes} = 1 \text{ hour and } 30 \text{ minutes}

Step 4: Calculate the final time

\text{9:00 AM} + 1\text{ hour }30\text{ minutes} = 10:30\text{ AM}

Answer: The three bells will ring together again at 10:30 AM (Option D)

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Q.286 Easy HCF and LCM

A shopkeeper buys books at ₹20 each and sells at a profit of 25%. During a sale, he gives a 10% discount. What is his effective profit percentage?

A 12.5%

B 15%

C 11.25%

D 13.75%

Correct Answer: A. 12.5%

Explanation:

To find the effective profit percentage, we need to track the cost price, marked selling price (with profit), and discounted selling price.

Step 1: Calculate the Marked Selling Price (with 25% profit)

The shopkeeper marks up books at a 25% profit on the cost price of ₹20.

\text{Marked Selling Price} = \text{Cost Price} + 25\% \text{ of Cost Price}

= 20 + 0.25 \times 20 = 20 + 5 = ₹25

Step 2: Calculate the Actual Selling Price (after 10% discount)

During the sale, a 10% discount is given on the marked price of ₹25.

\text{Discount} = 10\% \text{ of } 25 = 0.10 \times 25 = ₹2.50

\text{Actual Selling Price} = 25 - 2.50 = ₹22.50

Step 3: Calculate the Effective Profit

\text{Profit} = \text{Actual Selling Price} - \text{Cost Price}

\[= 22.50 - 20 = ₹2.50\]

Step 4: Calculate Effective Profit Percentage

\text{Profit\%} = \frac{\text{Profit}}{\text{Cost Price}} \times 100

= \frac{2.50}{20} \times 100 = \frac{250}{20} = 12.5\%

Answer: The effective profit percentage is 12.5% (Option A)

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Q.287 Easy HCF and LCM

Find the LCM of 48, 64, and 96 using prime factorization.

A 192

B 288

C 384

D 576

Correct Answer: A. 192

Explanation:

To find the LCM of 48, 64, and 96, we express each number as a product of prime factors, then take the highest power of each prime that appears.

Step 1: Prime factorization of each number

Divide each number by its prime factors:

48 = 2^4 \times 3^1

\[64 = 2^6\]

96 = 2^5 \times 3^1

Step 2: Identify all prime factors

The prime factors present are: \(2\) and \(3\)

Step 3: Take the highest power of each prime

- Highest power of \(2\): \(2^6\) (from 64)

- Highest power of \(3\): \(3^1\) (from 48 and 96)

Step 4: Calculate the LCM

\text{LCM}(48, 64, 96) = 2^6 \times 3^1 = 64 \times 3 = 192

Answer: The LCM of 48, 64, and 96 is \(192\) (Option A)

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Q.288 Easy HCF and LCM

A worker can complete a job in 12 days. Another worker can complete it in 18 days. If they work together, how many days will they take?

A 6.5 days

B 7.2 days

C 8 days

D 9 days

Correct Answer: B. 7.2 days

Explanation:

Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36; Time = 36/5 = 7.2 days

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Q.289 Easy HCF and LCM

A merchant offers successive discounts of 15% and 10%. What is the equivalent single discount?

A 23.5%

B 25%

C 24%

D 26.5%

Correct Answer: A. 23.5%

Explanation:

After 15% discount: 85%; After 10% on that: 85×90/100 = 76.5%; Single discount = 100-76.5 = 23.5%

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Q.290 Easy HCF and LCM

If a profit of ₹200 is made on a book by selling at 20% profit, what is the selling price?

A ₹1000

B ₹1200

C ₹1400

D ₹1500

Correct Answer: B. ₹1200

Explanation:

Profit = 20% of CP; ₹200 = 0.2×CP; CP = ₹1000; SP = 1000 + 200 = ₹1200

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